Doesn't sound like it would be easily to duplicate with any confidence, but if it was I'd say move the cable box in question near the display and running it for a hour. If it's multiple sources I'd feel pretty confident just using an Apple TV on wifi or something, but would definitly use copyright content. A single drop out means it has nothing to do with your HDBT, Power, Etc.

I had a similar problem with a powered in-wall soundbar. It got worse over time, finally bad enough to duplicate and it turned out to be the internal amp. Replaced, done, no call back.