This is very odd. Unfortunately I was not able to recreate this issue in my own testing. Creating an Ubuntu 17.10 x64 droplet, logging in and completing the password update and then running a reboot resulted in the droplets I tested rebooting and coming back online as expected. Please open a support ticket so our team can take a closer look at what you’re seeing.

I got a response from ticket support. Because from a user perspective it is unexpected behavior, I post it here to help other users who have this situation:

This is the response from ticket support:

• I did some testing with two Droplets - one with an SSH key and one without - but I haven't been able to reproduce that problem, I'm afraid. The problem could be related to changing distributions when you rebuild the Droplet though. Rebuilding uses the same settings from when the Droplet was first created (CentOS, it seems, judging by your Droplet's name), so if you're changing distributions like this the better approach would be to create a new Droplet. *

So rebuilding doesn’t seem to work as expected when switching from distribution.