b_hackbarth,
The UPS should clean up any brown-outs that comes to it, but if it is happening a lot your UPS may be having issues when it switches over causing problem with the system.
Have the customer unplug the UPS and verify that it stays up and the system doesn't go down.
You could also get a power tester setup on their circuit to see if there are power issues over a week. We actually had one customer that had all of their break room appliances on the same circuit as the phone system. Everyday at lunch time when the microwaves were used the phone system would have problems with power. This is why we state the system needs to be on a dedicated and circuit so that other devices don't cause issues with the power to the system.
Thanks,
TE