I meant to add that the bulk cipher my client is using to connect to the site is 128 bit AES

@Jubal

You may want to extend the configuration by adding:

SSLProtocol all -SSLv2 -SSLv3
SSLHonorCipherOrder on

… above the SSLCipherSuite directive. What you’d end up with is:

SSLProtocol all -SSLv2 -SSLv3
SSLHonorCipherOrder on
SSLCipherSuite AES256+EECDH:AES256+EDH:HIGH

…

That being said, I would recommend using what’s provided by https://cipherli.st:

SSLCipherSuite EECDH+AESGCM:EDH+AESGCM:AES256+EECDH:AES256+EDH
SSLProtocol All -SSLv2 -SSLv3
SSLHonorCipherOrder On
Header always set Strict-Transport-Security "max-age=63072000; includeSubDomains; preload"
Header always set X-Frame-Options DENY
Header always set X-Content-Type-Options nosniff
# Requires Apache >= 2.4
SSLCompression off 
SSLUseStapling on 
SSLStaplingCache "shmcb:logs/stapling-cache(150000)" 
# Requires Apache >= 2.4.11
SSLSessionTickets Off

…

It’s important to keep in mind, the ciphers that you list in SSLCipherSuite will only be used when they are supported. If the connecting client does not support them, it’ll cause an error.