Thanks, folks. I'll take a look at the Fios ONT box outside. I don't know how/if Verizon grounds those things on the coax side.

I don't think the cable box its self is the problem. It's a Tivo Bolt and isn't very old.

I just remembered something. A while back (can't remember how long), I was starting to get some really weird behavior from my Tivo recordings. A lot of cut-outs, garbled video, and incomplete recordings. Eventually I called either Verizon or Tivo and they recommended simply unscrewing the coax from the back of the box and screwing it back in. They said it releases some static buildup or something. It did fix that problem. Sounds like it could be related, no?
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Matt