This is a very difficult problem to diagnose sight unseen.
There could be a dozen interference issues that might not be obvious to someone with minimal experience in RF transmission.

As for getting the cable company to come out and test this is a great idea and it would be up to them to quote you a price on this but make sure theyare thorough if they do come out. Check major appliances (fridges, laundry etc) as well as your phones and any thing else in the house that MIGHT cause RF interference.

Have to go now, will try to respond later.