Here's my story from a few weeks ago, similar to yours. Took my car with the original sensors mounted in aftermarket wheels (for the past 65K miles) to a shop to fix a tire with a nail. The shop broke the OEM sensor and replaced it with an aftermarket one and programmed it. Blinking light then solid. So the shop replaced the sensor with another aftermarket and programed it. Same result.
Ended up having to take it to the dealership...they couldn't get the aftermarket sensor to program either. They put in a factory sensor and $290 later all is good. Even better, the shop paid for it.
Made me wince every time they put my pristine wheel on the mounter however....
Hard to believe the dealership expects me to spend almost $300 just to replace a sensor. Told me I should have brought it them first...just to patch the tire. About half that cost was the sensor. Guess that's why I never go to the dealership!