From reading breser's post, and from reading others' posts elsewhere, it sounds like this has nothing whatsoever to do with throttling. If it were a throttling issue, a simple reboot would not resolve the issue. I think breser is exactly correct: as I understand it, and in layman's terms, there is some sort of intermittent bug that prevents the connection to the servers when connected through wifi. Based on reports in other threads, I'd say this has absolutely nothing to do with VT.
I'm pretty sure that Tesla is aware of this bug too. I sent them a bug report about this and detailed all the things I did to diagnose this and explained that ultimately it was resolved by the touch screen reboot. Tesla responded with a very canned response telling me to reboot the touch screen and a picture showing how to do it.
The important bit of there email is this sentence
Please perform a touch screen reboot to reinitialize the network settings (picture instruction is shown below) and then try to reconnect with myTesla mobile application.
Based on this and the behavior I saw I'm pretty sure that the problem is that the routing table was busted for the wifi network interface and so traffic was probably not being sent properly. I've seen this with computers from time to time. So it's not terribly surprising to me.
I'm positive this has nothing to do with throttling because VisibleTesla and the apps will immediately start working if you disable the wifi. And then immediately stop working when you enable it again. On top of that I've observed that no traffic to/from Tesla was actually occurring in this state. If there was throttling I'd expect the car to still be able to connect to Tesla and communicate with them. They have complete control over what the car does and I don't see any reason for them to mess with that behavior. But the car was unable to talk to Tesla. If nothing else this same issue presents a problem for Tesla in being able to reach the car for their own diagnostic reasons.
If you're curious about how the network communications work and want some details then keep reading...
For the most part all communications with the car have to be initiated by the car. The reason for this is that the car may be behind a network that has a NAT or firewall that prevents connections from being made to it. This is a pretty standard behavior these days for a network to disallow connections that aren't specifically configured to be allowed to go to various devices. But outbound connections are typically not limited.
So whenever the car is on and running it connects to Tesla and has a VPN to them. Over this VPN then Tesla can initiate connections to the car. Basically the inbound communications are tunneled over an originally outbound communication channel. If the car can't open that communication channel then Tesla can't reach the car.
I'm not entirely clear how the car is woken when it's asleep. I haven't looked into how that works too much but my guess would be every so often the car wakes up, connects into Tesla and sends a message basically asking "Should I wake up?" Tesla then says yes and then the car wakes up and brings up the VPN to allow the app and everything works from there.
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Another bit of proof it's not related to VisibleTesla. Everything was working fine last night with the Android App when I went to bed. Got up this morning and it's back to doing it again. Realized that VisibleTesla wasn't running since yesterday sometime because my desktop had crashed. I know it was crashed when I came home but I didn't think about it. So between me restarting the touch screen and it breaking again this morning, VisibleTesla wasn't being used at all. Restarting the touch screen resolved the problem again. Tesla has some sort of bug.