I have ridden BART most workdays for the past 7 years. I have encountered trains with stuck doors a several times, and on none of those occasions was the train put out of service. In fact, they even have pre-printed stickers that say something to the effect of "This door is not working; please use other door." I have seen these perhaps half a dozen times since I began riding BART regularly.

Note that these doors were stuck _closed_. It would be an obvious safety hazard if the door was stuck open - in that case I can well imagine that the operator would not move the train from the station.