Mud,
The modems used by Unitec are essentially US Robotics modems, however, they contain your CC merchant info, so you can't just swap them out with another brand/type. But if your CC processor modems don't accept USR modems, it would be like your carwash not accepting Fords.
Has anyone dialed into your modem and did any troubleshooting? Its rather easy to do and they do keep some logs (like it will tell you why it failed in any communications)?
You seem to be going around in circles with this stuff, instead of finding someone who can help you get this resolved. I personally think that the processor's modems (likely virtual modem bank) is having problems (since you have multiple locations having the same problem). I would try changing the Initialization string (Init String) of the modem (tells it how to behave, what protocols to use etc) based on what the modems are seeing and what config your merchant uses and the protocols it will accept. If this is set correctly, your connections will be quicker (no need to try and handshake to a bunch of protocols one end won't support) and more stable connections.
An IT guys who knows modems and 1HR and all your problems are fixed. How many hours are you going to continue spinning your wheels?