I use Transmit, but have it set to SFTP. My user in the panel is set to be a Shell account and I've disallowed FTP. I recommend the same setup for you, as SFTP is more secure.
1) Edit your Transmit setting to be SFTP
2) Go to the panel here for Manage Users and click Edit for your user. Set it to SFTP or Shell and disallow FTP.
3) While you're at it, set that user's password again and then click Save Changes.
And for better insight into the problem, turn on Transmit's "Transcript" window under the window's menu to watch the login happen and see what's causing the error.