Worth a shot having someone in Verizon's Fiber Solutions Center pull up the ONT logs and stats to see if there are some signal issues with the Fiber. Alternatively, you may want to consider checking your coaxial stats and connections if both TV and Internet come over the Coaxial cables. The FiOS router does give you some idea of how your MoCa connections are running.
Here's something you can check: https://secure.dslreports.com/faq/16569