Older Model S and X (2017 and earlier, the original car computer) switch WiFi off when they go to sleep and only rejoin it when something wakes the car from the inside: a door, the key, a scheduled charge. While asleep on WiFi the car is unreachable from the internet, so Tesla's servers and mytesly see it as offline, and nothing can wake it remotely. On a car with cellular service the modem stays on in a low-power state and that is the path remote wake-ups use. With no cell coverage at home there is no such path. A 2017 car also shipped with a 3G modem; 3G networks shut down in 2022, so without Tesla's LTE modem upgrade the car has no cellular anywhere.

What you can do: turn on Always Connected (Controls, Display, Energy Saving on pre-2018 S/X). It is meant to keep the car reachable while it sleeps, at the cost of a little more overnight drain, about one percent a day. If the car still drops off WiFi in sleep, Tesla's LTE modem retrofit is the fix; it is a service-centre job. Newer cars (2018 on, and any car with the infotainment upgrade) are not affected the same way.

What mytesly does: it never wakes the car on a schedule or for data. A wall-button press or an app action wakes the car once and keeps retrying for a few minutes. A car that has dropped off WiFi in sleep cannot be reached at all until something wakes it from the inside.