One user can use SSHFS, other user gets "remote host has disconnected"

From the OpenSSH FAQ (via knoppixforum.de, English translation here):

sftp and/or scp may fail at connection time if you have shell initialization (.profile, .bashrc, .cshrc, etc) which produces output for non-interactive sessions. This output confuses the sftp/scp client. You can verify if your shell is doing this by executing:

ssh yourhost /usr/bin/true

If the above command produces any output, then you need to modify your shell initialization.

Also try ssh user@host /bin/true.

I got it working... The permissions on the user's home folder were set incorrectly. Apparently this doesn't prevent ssh login, but does break sshfs.