Yow! This is a pain and I bet it's going to happen to more people. I bet I know what you two did--and it didn't have anything to do with fiddling with your password. It was the other thing you changed: your shell. If my guess is correct, you, like me, installed bash as well as dropbear (which, by the way, just starts it; it's already on the box). Then either you symlinked bash into /bin/ or you modified the passwd file to point at /mnt/DroboShares/....
Sooo... I did this. And then, before logging out, I tried to log in in another tab. After a bunch of fiddling around (and no love from Google except this page), I figured out that changing the shell back to /bin/sh allowed me to log in again. Changing the password is not a problem.
On a fully-fledged box, there would be an /etc/shells file that listed login shells, but there is no such file on my DroboShare.
So far, I haven't figured out how to get DroboShare to execute bash on the Drobo mount.
But back to passwords... In addition to changing your password, you can instead use an ssh authorized_keys file. Both rsa and dss public keys work, but note that the name authorized_keys2 won't. And your .ssh directory (and/or?) authorized_keys file need(s) to be mode 600, which probably won't happen by default because there is no umask command in /etc/profile, so typically your umask is 0 instead of the typical 22.