Ok, I opened my Sim slot on my Verizon 4S (yes, Verizon) and found a white Verizon Sim card. I removed the Sim and the phone is working fine so far.

I have been getting the same "Sim Failure" messages on my Verizon iPhone 4S. Yesterday it happened 3 times in a row. Previous to that it was 2 times since I got the phone. I have to power it down and up to get service after I get this error.