...which of course has the phone company saying it is on our side.
We refer to this as MBSWWYPBX.

Hi Austin, and welcome to the board.
I see you're out of Ft. Worth. I haven't thought of Source One in a while, but I think Ken (here on the board) did a lot of business with them.
Several things come to mind, but if you work on Inter-Tel you're probably familiar with several of these things.
First off, the Axxess does not like low voltage or a bad ground. Check your UPS units if using one, and make sure the cabinet is grounded properly.
Next are some basic troubleshooting questions.
Does it happen from more than one extension?
Does the office have enough extenstions that you're using more than one station card?
If so does it happen from the extensions on more than one station card?
What about line cards?
The same questions apply.
Have you reset the cabinet?
Also have you checked line voltage?
We'll start with this, but may need to move this thread if we get too deep. It looks like I'll be at the computer most of the evening and I'll get Ken to chime in with his 2 cents as well.