Incandescent to LED change
I have experienced problems with the bulbs not screwing all the way in, usually due to the shape of the LED bulb not being quite the same as an incandescent bulb, and at least once from malformed threads. 

Since your bulb works in other fixtures, I'd bet on the one fixture having something that the LED bulbs are sticking on before they get all the way in, or that the center contact has been flattened by some previous bulb and needs (with the circuit breaker for this circuit off, please) to be gently bent/pulled up; or in case of severe damage, replace the socket, or the fixture.