Here is a small one that drove me crazy once. Almost the same thing was being complained about...it turned out to be that on the opposite side of the wall in the next suite, a dentists office, was there X-ray equipment on the wall. Everytime they took a picture it would cause RF or EMI and the our customers KSU would glitch. some times calls would drop but mostly the calls in progress would here a white noise that quickly got louder and then as quickly went away. It took us a while to figure this out, we changed KSU's, ran new grounds, had electrician in.

Air compressors will lose air overnight and recycle some of the times so its not uncommon for a air compressor to kick on at odd times.

We also had a building issue in a strip style office park where the huge on the ground transformer just outside the customers back door was causing power issues for several customers. They came out and repaired something and everything was fine. The electrician discovered this one. Also a machine shop's electric welder caused problems once that was solved by using shielded cable for the shop phone.