System 5.436.
When dialing into this system, we get connectivity and the screens says 'Logging In'.
After a few seconds, however, the modem suddenly drops the connection and the system says 'Database Connection Failed'.
Any ideas what is causing this?

Try the standard; reset the modem at the other end. maybe reset the System. You may also have a bad comm port on the System.

try a lower baud rate on your calling modem. Make sure that msg pring and smdr are not being sent out the same port that your modem is connected to; this will kill a modem every time.