My auto-close very seldom works (and has been that way since I got the vehicle). It actually seems more likely to activate when I don't want it to than when I do (i.e. parking in the driveway and then moving the vehicle to get in the garage). Regarding the times when it doesn't work, I don't think it's related to hitting the brake on the way out or putting it in reverse after pulling in, as I do these things every time and it does work on rare occasion. Someone had posited in an earlier thread that it might only work when the center screen has not been touched, but I can confirm that is not the case for me, either. I had figured it might be an issue with going into reverse and/or starting to move too soon, because it seemed to me like when I would sit in the can for a bit before taking those actions it would work, and I can't rule that out, but sitting in the car for a short period of time doesn't consistently make mine work. However, I can also confirm that it has worked when I was in the garage and opened the garage door from the wall as well as when I have opened the garage door from the center screen. Moreover, triggering homelink is triggering homelink, so I don't think there is any check for state intended (except maybe using summon, and I would assume it would use radar to check).
In my personal opinion, Tesla's decision to purchase a Homelink module instead of making their own software may have been a mistake. I don't know enough about garage door openers to be sure on this, but I would like to have more the ability to open more than three garage doors, and I assume that arbitrary limit is due to the Homelink's module design as opposed to any other sort of hardware limitation.
To all those people guessing maybe it's GPS related, the garage doors that are close per GPS show up green while the other ones show up white, so you can tell by looking at the screen whether or not GPS knows you're near the garage door.
To all those people guessing it's structural, when auto-open and auto-close are to be activated, the center screen shows the opener list, indicates how many feet until the task will occur, and has a skip button available in case you don't want it to. In my case (and most likely the OP's), the issue is that there is no indication of feet until auto-close or skip button because auto-close simply hasn't been initiated by the vehicle.