iPhone 5 Verizon LTE problem

I have the 64GB iPhone 5 in white on the Verizon network.  Each day at a random time LTE will have a problem where I can't make a facetime call.  If I try and run a speed test either my up or down will not complete the test.  The only way for me to fix the issue is to toggle airplane mode and as soon as my phone picks up the Verizon LTE signal I can make a facetime call.

I have done some troubleshooting on my own and here are some of those steps and results.

I contacted Verizon and they "rebuilt" my line in their system.  I'm not sure what that means, but Verizon assured me it would fix any issues in their systems. 

I have the issue on LTE only, 3G and Wifi have no issues with facetime and complete speeds tests every time without issue. 

LTE in my area is a full 5 bars and when I'm not experiencing this issue I typically get 10-20Mb down/up

I contacted AppleCare and they suggested I do a reset.

I tried a reset on "Network Settings"

Nothing above has made any progress so tonight I'm trying a full reset on the phone per AppleCare instructions.  If that doesn't work I was told to take the phone into an Apple store.  The only issue with that is the 1 hour drive one way which I'm trying to prevent.

If anyone else is having the same issue please speak up or point me to a fix you have done. 

Thank you,

Tom