Just in case this is not already difficult enough ...

Consider that a problem with the central locking system - completely independent of the wireless / remote subsystem - could be causing problems.

Is everything else in your locking system working perfectly? E.g., button in central console - do all door lock actuators reliably and powerfully lock and unlock when commanded? Controlled by door buttons? Do windows control as commanded?

I once had a problem with my 2001 3.0i where a (thankfully not intermittent) electrical problem with my driver's door lock actuator caused flakiness in other parts of the system (including rear door lock actuation) and complete failure of the remote entry functionality. Summarized in a thread on here somewhere. As soon as I swapped back in my mechanically cracked, but electrically good driver's door lock actuator, everything was rock solid - keyless entry, rear door lock actuation, etc.

Whatever you do, make sure your mechanical door key cylinder does not fail and leave you locked out, as they often do when needing increased usage when the remote entry dies or becomes flaky. It seems the key cylinder lasts about a year of daily usage before failing.

If you had not taken your keys to a pro, and if you do not have any other locking control problems, I'd expect the keys to be the issue. But ... now it becomes a question of what kind of testing the pros did, and how much faith you have in anything they did.

Another option that may be helpful for debugging is to buy a remote key / fob on eBay. I bought 3x of used BMW diamond keys when I first got my X5, using them as fobs on keychains with non-remote Genuine BMW keys. It seems those are no longer sold there, but brand new Chinese eBay knockoffs are. Surely the EWS will not work on those (despite claims) but the remote functionality should, and is easy to program following the standard sequence. So as a test, and as a future backup, you could get one of those, program it, and evaluate its reliability. If it is rock solid, then that confirms key flakiness as the problem. If still flaky, it points elsewhere.

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2001 X5 3.0i, 203k miles, AT, owned since 2014