Have you tried either calling Apple for support or going to your local Apple Store (if one is in your area) to get help. If it's a device setting issue or if it's a problem with your backup (if you set up your device using a backup versus setting it up as new) then they will be able to figure out the problem. Not sure if you are a new Verizon customer and ported your number over but if you did that sometimes seems to happen with ports...in which case you may need to contact Verizon to make sure everything is set up correctly on their end. Of course if you've been a customer that shouldn't apply to you. Other suggestions tend to be to replace the SIM card if they think that's the issue. But if you feel like you've done everything including contacting technical suppport with Verizon and contacting Apple for support (phone, online, or in store) then I'm not sure what the next step would be other than them replacing the device (don't think it's a hardware issue though).