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).