It's possible you're running afoul of a change in the RF security protocol for the opener. Happened sometime in the aughts (2005-2010'ish). I'm vague on the details but I believe Homelink changed their protocols to accommodate the new protocol, therefore not all years/models of BMW's will have the same level of compatibility.
We've also experienced similar things to what you're seeing with similar cars, since we had an '02 X5, '02 330i, '12 X5, '14 335i. We were having some work done on the garage door opener once and the repair guy installed a homelink repeater which took care of the weirdness. I also never solved weirdness with our neighborhood gated entry - that remote programmed easily with all of our cars except never would work with the F30. It would show all the right signs of having taken the program but just wouldn't work.
Anyway, Google "homelink repeater" and you'll see what I'm talking about. If you call homelink and they determine you need one, they'll send you one for free.
https://www.amazon.com/hyd_sl_lpo/7b...wd-57396260142