I had this same issue, tried replacing back cover, battery, 4g sim card and nothing worked. Verizon claimed no network issues.
I ended up asking for a replacement unit (under warranty) and the replacement unit does not have the same problem.
Lesson is, 4g hardware for the Thunderbolt can fail spontaneously. Mine degraded gradually like yours to **** over a period of a few weeks. My 3G was also affected, so it may have something to do with the qualcomm chipset itself.
In any case, try a new sim card but dont be shocked if it doesn't work and you have to get a new phone. Hope you are under warranty