Sorry to learn of this issue, let's get it fixed! When did this begin? Have you tried removing and reinserting the SIM card?
Follow us on Twitter @VZWSupport
Sounds like you may have either a falty SIM card or there may be something wrong with your sim slot. Try reinserting the sim to see if it helps. Otherwise you may need a replacement card (assuming the card is bad) or your device may need to be replaced. First need to rule out the SIM card itself to make sure that's not the problem.
I had this very same thing happen to me with my iP5. Went to VZW to get a new sim, that didn't work, went to the Apple Store to see if they could diagnose the issue...no such luck. After about 5 minutes of messing with it at the Apple Store, the tech just decided to replace my phone. Thank goodness I was still within my AppleCare warranty.