I had a cold solder joint that was working sort of intermittently in one of my crossovers that caused a speaker of mine to do the same thing...mine was at a speaker terminal lug on the crossover.
It might be something with the xo...
Try it in a different room. Is your cable coming in/out of your amplifier in securely? Try switching that (ya never know, I've had it happen to me...). If the problem persists you can bet it's something with the speaker.

The crossover and tweeter are easy enough to replace in those if it comes to that. They might find when removing the tweeter that the quick disconnect or solder joint are the culprit.

Whatever you do...DON'T let this drag on...every trip to the dealer and back is money out of your pocket.