Good advice has already been given, however, in order to determine if there’s a specific share causing the issue, I’d suggest two things:
1) Create a new blank user, connect from there and try to see if this new user exhibits the same problem/behavior.
2) Additionally, disconnect all shares and start connecting one by one and perform the voodoo magic to reproduce the “disconnect” dialog (with each individual connection). That way you could see if the problem only manifests in some connections but not others, or all.
Do you have any server log or anything that could be an indication of a process hanging or waiting for a server response that never comes? (already suggested)
UPDATE: Today I made a test. I connected my 10.6.4 to a Samba box running an ancient version of Fedora (probably 3-4 years old). And when I had the connection open, I halted the server to get the Server connections interrupted dialog:
Here’s how my dialog looked like:

public is the name of the share and nippur is the name of the server.
Now that’s why your dialog looked weird. Are you sure you’re running 10.6.x?
UPDATE 2: You’re running 10.6.4 but using ADMitMac, which "turns a Mac into a true Active Directory client”. I suspect that’s where the problem lies. I’d disable or remove that and start from there. I’m 99% sure that without it, the problem will go away. The problem will then turn onto a new question… why? But that’s an entire new world and only Console Logs will help (plus, of course, ADMicMac’s tech support).