Interesting problem. The whole point of getting "cable" instead of satellite is to be able to have service during inclement weather. It sounds like you've done a pretty good job of troubleshooting the issue already.
If I were you, I would try one more thing to help isolate the cause of the problem. When your service is working, and it is dry outside, I would use the hose or sprinkler on the exterior ONT. (Just be careful if you are holding the hose while doing this test to make sure that you are not wet/barefoot/grounded. If it is a full electrical short, you don't want to find out the hard way.) If your service drops during this test, you know the cause. And if you have a Verizon wiring maintenance plan, it should not cost you anything regardless of where the problem lies.