After trading about 20 messages over several days through the app with my local SC and setting up an appointment for them to work on my car, they ended up cancelling the appointment and told me that while replacing the connectivity card might fix the issue, they believe it can also be fixed with a software update, since that is what likely caused it to break in the first place.The reason you can connect to it everywhere other than your home is likely because you probably have Sentry Mode enabled, but configured not to be used when the car is at your home. Sentry Mode would keep the car from going to deep sleep.
I have the exact same problem with the app not connecting to my MY. It won't connect to it when the car is at home or at work (because Sentry Mode is not enabled for both of those locations) unless the car is not asleep. This issue started for me about 3 weeks ago. I've tried logging out of the app, uninstalling and reinstalling the app, updating the app, rebooting the car (holding both buttons while pressing the brake pedal). Nothing fixes this. My girlfriend has the exact same problem with the app on her phone also not able to connect to the car when it is asleep.
This morning I finally got fed up with it and created a service request with Tesla through the app. I haven't heard back from them yet, but my appointment is scheduled for Tuesday the 25th.
I read in another thread that someone else having similar issues had a part swapped out on their car by Tesla mobile service and that resolved it. The poster referred to the part as a "connectivity card".
For what it's worth, my car is a 2021 MYLR running 2022.20.18 (FSD 10.69.2.3).
"...this concern is currently under review by our Service Engineering team and at this time an onsite visit is not necessary...
Generally with firmware related concerns, there is a process to identify them as rooted in firmware and that usually comes at the expense of testing, that may include hardware replacement. As our Service Engineering team continues with root cause analysis they will be providing guidance to stop replacing hardware and collect as much information as possible. At this point this concern is still under investigation and we hope to have a fix relatively soon...
We have forwarded our findings to the Service Engineering team and the fix for this concern will be an OTA update."