FYI, to those who've followed this thread, the outcome was as follows: I had a visit from two of Tesla's top people in the Caribbean, one of them an engineer who understood the system perfectly. When he realized we were basically running disconnected from the grid, he said Tesla was probably in the system at some point, making adjustments or upgrading and then set it to reboot, so it shut down, but because the grid is off, it can't 'jump start' itself. It can't use the battery to jump start the system. So it remains off until I let the grid in and then it reboots. That was the explanation and it fit all scenarios perfectly. They have not upgraded our firmware in a while and we have not had shutdown problems for over a year now.
About the cellphone connect/disconnect issue, the installers techs were here recently, they could find no problems with the setup and it is using the best firmware version for our equipment. And no, they could not disable the cell connect but they really didn't know what it was for and how exactly it worked. Not their paygrade. However, I can not get a straight answer out of Tesla about whether they need this cell connect or not, and can it be disabled. No answer yet. I'm going to try again. There's definitely a loose screw or two in their circuitry but they don't seem to want to hear about it.