No, they don't break down all the time. There's a reason their resale value's the highest. The parts can be expensive (maintenance or repairs) compared to non-luxury cars. However, if it's under warranty, you're good for a long time. BMW comes with maintenance included. It's the only one that has a true included maintenance. Only thing that's not covered is tires. Windshield wipers, brakes, all those other wear and tear items are covered.
Once it's out of warranty, just go to an independent service person that does BMWs. Then, it really isn't any more expensive than if someone with another brand took their car to the dealer to be serviced. Or, you can just do the work yourself. It's not like the cars are particularly complicated or anything.