Some questions to help get the topic rolling:
1) Are multiple users being disconnected at the same time or is it one or two at a shot?
2) Is the problem happening with the same extensions or is it spread out across all users?
3) When the calls drop, do the displays on the phones go blank?
4) Is the system on a UPS?
5) Can you connect SLTs to the demarcs and duplicate the problem?
6) Can you verify the current being delivered to the system from Cox's equipment to make sure it is within accepted limits?
7) Is there any equipment being used that could generate interference that would cause the system to reset?
8) I think that the ACS has an alarm/error log. If it does, can you check it to see if it yields any clues?
If it ain't broke, I haven't fixed it yet.