The problem certainly could be caused by an electronic component, but it is likely that there is subsequent consequential damage. I say that because of your comment that the oil smelled burnt, and had particles in it (likely friction material). An electronic failure can cause low clutch pressure, that causes slippage, that makes heat (and clutch plate debris) and then you're stuffed.

BMW doesn't repair these transmissions because they don't make them, they simply buy them from either ZF or GM. They consider them sealed components, and don't train their dealers to work on them, or stock parts for them. Transmission shops familiar with your model of transmission (which will be used in lots of vehicles other than BMW) have the training, tools, manuals, and parts sources to rebuilt them. That kind of shop is what you need to find.

You could drive it until it leaves you on the side of the road, but at that point you may not be able to get it home, it may not be convenient, and it may not be safe (depends where it leaves you). I would start researching transmission shops, and have it overhauled when it is convenient to do so. It isn't going to fix itself.

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2007 X3 3.0si, 6 MT, Premium, White

Retired:
2008 535i, 6 MT, M Sport, Premium, Space Grey
2003 X5 3.0 Steptronic, Premium, Titanium Silver
2002 325xi 5 MT, Steel Grey
2004 Z4 3.0 Premium, Sport, SMG, Maldives Blue