As far as I can tell, the reason is:
when a miner is on standby for a longer time (exiting the game and come back) it defaults with his drill head parked out of the drill whole. If you now just take a tiny bit of ore out of it, the animation and the sound will start to bring the drill head back in the whole. But before the miner can finisch that, the ore is filled up again, hence it gets stuck in the middle of the "drill head in whole" process and the sound keeps playing.