The razr/maxx shouldn't be power cycling.... shut it off and remove the sim and SD card. Look at both of them, make sure the sdcards connection area doesn't look oxidized(dull) if so, gently clean it with an eraser from a pencil. And re insert it.
The sim, if it looks damaged, or scratched too deeply, go to a vzw store and get a replacement.
Welcome to DF. Is this very recent? Anything different that you have done to your phone just before it started happening. Try 94lt1's suggestion. If you haven't done an fdr since upgrading to ICS, one may be in your future. It does make a huge difference.
100% concur. There's no reason for the RAZR/MAXX to power cycle. I haven't had mine do it once that I am aware of, since getting the RAZR in late winter, and the MAXX in mid summer.