Why is my droplet still asking for a password when I have added the SSH key?

What worked for me:

ssh root@<ip>

Because I’m logged in on my local machine as user ‘tjen’, and ssh <ip> then it asks for: tjen@gtd's password:, (which does not exist)

wow this is very informative post

Same issue here:

mathew@Mathews-MacBook-Pro:Documents -->rsync -avz provisioning/ root@xxx.xxx.xxx.xxx:/root/
building file list ... done
./
iptables.conf
iptables.sh
provision.conf
provision.nginx-gw.sh
provision.sh
provisioning/
provisioning/iptables.conf
provisioning/iptables.sh
provisioning/provision.conf
provisioning/provision.nginx-gw.sh
provisioning/provision.sh

sent 28754 bytes  received 252 bytes  19337.33 bytes/sec
total size is 58582  speedup is 2.02
mathew@Mathews-MacBook-Pro:Documents -->ssh root@xxx.xxx.xxx.xxx
root@xxx.xxx.xxx.xxx's password:

Key worked, then immediately didn’t. Running ssh -vv gives no error:

mathew@Mathews-MacBook-Pro:Documents -->ssh -vvv root@xxx.xxx.xxx.xxx
OpenSSH_6.9p1, LibreSSL 2.1.7
debug1: Reading configuration data /Users/mathew/.ssh/config
debug1: /Users/mathew/.ssh/config line 1: Applying options for *
debug1: Reading configuration data /etc/ssh/ssh_config
debug1: /etc/ssh/ssh_config line 21: Applying options for *
debug2: ssh_connect: needpriv 0
debug1: Connecting to xxx.xxx.xxx.xxx [xxx.xxx.xxx.xxx] port 22.
debug1: Connection established.
debug1: identity file /Users/mathew/.ssh/id_rsa type 1
debug1: key_load_public: No such file or directory
debug1: identity file /Users/mathew/.ssh/id_rsa-cert type -1
debug1: key_load_public: No such file or directory
debug1: identity file /Users/mathew/.ssh/id_dsa type -1
debug1: key_load_public: No such file or directory
debug1: identity file /Users/mathew/.ssh/id_dsa-cert type -1
debug1: key_load_public: No such file or directory
debug1: identity file /Users/mathew/.ssh/id_ecdsa type -1
debug1: key_load_public: No such file or directory
debug1: identity file /Users/mathew/.ssh/id_ecdsa-cert type -1
debug1: key_load_public: No such file or directory
debug1: identity file /Users/mathew/.ssh/id_ed25519 type -1
debug1: key_load_public: No such file or directory
debug1: identity file /Users/mathew/.ssh/id_ed25519-cert type -1
debug1: Enabling compatibility mode for protocol 2.0
debug1: Local version string SSH-2.0-OpenSSH_6.9
debug1: Remote protocol version 2.0, remote software version OpenSSH_6.6.1
debug1: match: OpenSSH_6.6.1 pat OpenSSH_6.6.1* compat 0x04000000
debug2: fd 3 setting O_NONBLOCK
debug1: Authenticating to xxx.xxx.xxx.xxx:22 as 'root'
debug3: hostkeys_foreach: reading file "/Users/mathew/.ssh/known_hosts"
debug3: record_hostkey: found key type ECDSA in file /Users/mathew/.ssh/known_hosts:71
debug3: load_hostkeys: loaded 1 keys from xxx.xxx.xxx.xxx
debug3: order_hostkeyalgs: prefer hostkeyalgs: ecdsa-sha2-nistp256-cert-v01@openssh.com,ecdsa-sha2-nistp384-cert-v01@openssh.com,ecdsa-sha2-nistp521-cert-v01@openssh.com,ecdsa-sha2-nistp256,ecdsa-sha2-nistp384,ecdsa-sha2-nistp521
debug1: SSH2_MSG_KEXINIT sent
debug1: SSH2_MSG_KEXINIT received
debug2: kex_parse_kexinit: curve25519-sha256@libssh.org,ecdh-sha2-nistp256,ecdh-sha2-nistp384,ecdh-sha2-nistp521,diffie-hellman-group-exchange-sha256,diffie-hellman-group-exchange-sha1,diffie-hellman-group14-sha1,diffie-hellman-group1-sha1
debug2: kex_parse_kexinit: ecdsa-sha2-nistp256-cert-v01@openssh.com,ecdsa-sha2-nistp384-cert-v01@openssh.com,ecdsa-sha2-nistp521-cert-v01@openssh.com,ecdsa-sha2-nistp256,ecdsa-sha2-nistp384,ecdsa-sha2-nistp521,ssh-ed25519-cert-v01@openssh.com,ssh-rsa-cert-v01@openssh.com,ssh-dss-cert-v01@openssh.com,ssh-rsa-cert-v00@openssh.com,ssh-dss-cert-v00@openssh.com,ssh-ed25519,ssh-rsa,ssh-dss
debug2: kex_parse_kexinit: chacha20-poly1305@openssh.com,aes128-ctr,aes192-ctr,aes256-ctr,aes128-gcm@openssh.com,aes256-gcm@openssh.com,arcfour256,arcfour128,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,rijndael-cbc@lysator.liu.se
debug2: kex_parse_kexinit: chacha20-poly1305@openssh.com,aes128-ctr,aes192-ctr,aes256-ctr,aes128-gcm@openssh.com,aes256-gcm@openssh.com,arcfour256,arcfour128,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,rijndael-cbc@lysator.liu.se
debug2: kex_parse_kexinit: umac-64-etm@openssh.com,umac-128-etm@openssh.com,hmac-sha2-256-etm@openssh.com,hmac-sha2-512-etm@openssh.com,hmac-sha1-etm@openssh.com,umac-64@openssh.com,umac-128@openssh.com,hmac-sha2-256,hmac-sha2-512,hmac-sha1,hmac-md5-etm@openssh.com,hmac-ripemd160-etm@openssh.com,hmac-sha1-96-etm@openssh.com,hmac-md5-96-etm@openssh.com,hmac-md5,hmac-ripemd160,hmac-ripemd160@openssh.com,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: umac-64-etm@openssh.com,umac-128-etm@openssh.com,hmac-sha2-256-etm@openssh.com,hmac-sha2-512-etm@openssh.com,hmac-sha1-etm@openssh.com,umac-64@openssh.com,umac-128@openssh.com,hmac-sha2-256,hmac-sha2-512,hmac-sha1,hmac-md5-etm@openssh.com,hmac-ripemd160-etm@openssh.com,hmac-sha1-96-etm@openssh.com,hmac-md5-96-etm@openssh.com,hmac-md5,hmac-ripemd160,hmac-ripemd160@openssh.com,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: none,zlib@openssh.com,zlib
debug2: kex_parse_kexinit: none,zlib@openssh.com,zlib
debug2: kex_parse_kexinit:
debug2: kex_parse_kexinit:
debug2: kex_parse_kexinit: first_kex_follows 0
debug2: kex_parse_kexinit: reserved 0
debug2: kex_parse_kexinit: curve25519-sha256@libssh.org,ecdh-sha2-nistp256,ecdh-sha2-nistp384,ecdh-sha2-nistp521,diffie-hellman-group-exchange-sha256,diffie-hellman-group-exchange-sha1,diffie-hellman-group14-sha1,diffie-hellman-group1-sha1
debug2: kex_parse_kexinit: ssh-rsa,ecdsa-sha2-nistp256
debug2: kex_parse_kexinit: aes128-ctr,aes192-ctr,aes256-ctr,arcfour256,arcfour128,aes128-gcm@openssh.com,aes256-gcm@openssh.com,chacha20-poly1305@openssh.com,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,rijndael-cbc@lysator.liu.se
debug2: kex_parse_kexinit: aes128-ctr,aes192-ctr,aes256-ctr,arcfour256,arcfour128,aes128-gcm@openssh.com,aes256-gcm@openssh.com,chacha20-poly1305@openssh.com,aes128-cbc,3des-cbc,blowfish-cbc,cast128-cbc,aes192-cbc,aes256-cbc,arcfour,rijndael-cbc@lysator.liu.se
debug2: kex_parse_kexinit: hmac-md5-etm@openssh.com,hmac-sha1-etm@openssh.com,umac-64-etm@openssh.com,umac-128-etm@openssh.com,hmac-sha2-256-etm@openssh.com,hmac-sha2-512-etm@openssh.com,hmac-ripemd160-etm@openssh.com,hmac-sha1-96-etm@openssh.com,hmac-md5-96-etm@openssh.com,hmac-md5,hmac-sha1,umac-64@openssh.com,umac-128@openssh.com,hmac-sha2-256,hmac-sha2-512,hmac-ripemd160,hmac-ripemd160@openssh.com,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: hmac-md5-etm@openssh.com,hmac-sha1-etm@openssh.com,umac-64-etm@openssh.com,umac-128-etm@openssh.com,hmac-sha2-256-etm@openssh.com,hmac-sha2-512-etm@openssh.com,hmac-ripemd160-etm@openssh.com,hmac-sha1-96-etm@openssh.com,hmac-md5-96-etm@openssh.com,hmac-md5,hmac-sha1,umac-64@openssh.com,umac-128@openssh.com,hmac-sha2-256,hmac-sha2-512,hmac-ripemd160,hmac-ripemd160@openssh.com,hmac-sha1-96,hmac-md5-96
debug2: kex_parse_kexinit: none,zlib@openssh.com
debug2: kex_parse_kexinit: none,zlib@openssh.com
debug2: kex_parse_kexinit:
debug2: kex_parse_kexinit:
debug2: kex_parse_kexinit: first_kex_follows 0
debug2: kex_parse_kexinit: reserved 0
debug1: kex: server->client chacha20-poly1305@openssh.com <implicit> none
debug1: kex: client->server chacha20-poly1305@openssh.com <implicit> none
debug1: expecting SSH2_MSG_KEX_ECDH_REPLY
debug1: Server host key: ecdsa-sha2-nistp256 SHA256:aaku/+vSiPl9Y+qv0rUPXqZDQ5ejhAymF17BKWKobgg
debug3: hostkeys_foreach: reading file "/Users/mathew/.ssh/known_hosts"
debug3: record_hostkey: found key type ECDSA in file /Users/mathew/.ssh/known_hosts:71
debug3: load_hostkeys: loaded 1 keys from xxx.xxx.xxx.xxx
debug1: Host 'xxx.xxx.xxx.xxx' is known and matches the ECDSA host key.
debug1: Found key in /Users/mathew/.ssh/known_hosts:71
debug2: set_newkeys: mode 1
debug1: SSH2_MSG_NEWKEYS sent
debug1: expecting SSH2_MSG_NEWKEYS
debug2: set_newkeys: mode 0
debug1: SSH2_MSG_NEWKEYS received
debug1: Roaming not allowed by server
debug1: SSH2_MSG_SERVICE_REQUEST sent
debug2: service_accept: ssh-userauth
debug1: SSH2_MSG_SERVICE_ACCEPT received
debug2: key: /Users/mathew/.ssh/id_rsa (0x7fbe50500880),
debug2: key: /Users/mathew/.ssh/id_dsa (0x0),
debug2: key: /Users/mathew/.ssh/id_ecdsa (0x0),
debug2: key: /Users/mathew/.ssh/id_ed25519 (0x0),
debug1: Authentications that can continue: publickey,gssapi-keyex,gssapi-with-mic,password
debug3: start over, passed a different list publickey,gssapi-keyex,gssapi-with-mic,password
debug3: preferred publickey,keyboard-interactive,password
debug3: authmethod_lookup publickey
debug3: remaining preferred: keyboard-interactive,password
debug3: authmethod_is_enabled publickey
debug1: Next authentication method: publickey
debug1: Offering RSA public key: /Users/mathew/.ssh/id_rsa
debug3: send_pubkey_test
debug2: we sent a publickey packet, wait for reply
debug1: Authentications that can continue: publickey,gssapi-keyex,gssapi-with-mic,password
debug1: Trying private key: /Users/mathew/.ssh/id_dsa
debug3: no such identity: /Users/mathew/.ssh/id_dsa: No such file or directory
debug1: Trying private key: /Users/mathew/.ssh/id_ecdsa
debug3: no such identity: /Users/mathew/.ssh/id_ecdsa: No such file or directory
debug1: Trying private key: /Users/mathew/.ssh/id_ed25519
debug3: no such identity: /Users/mathew/.ssh/id_ed25519: No such file or directory
debug2: we did not send a packet, disable method
debug3: authmethod_lookup password
debug3: remaining preferred: ,password
debug3: authmethod_is_enabled password
debug1: Next authentication method: password
root@xxx.xxx.xxx.xxx's password:

In this case it definitely appears to be a bug.