The car appears to be going to sleep since I see the dash doing its ~11 second wake up, and Visual Tesla gives me the sleep warning if I open that app while the car is sleeping. I did try rebooting both screens when we returned from the trip yesterday.
In addition to rebooting the screens, you may want to try pulling the screen/3G connection fuse. Not sure what if it'll help, but it's worth a shot. Let us know if and how you manage to fix it.