Is it a Dusty dulcimer? What model? Unless the tuning pins feel really loose, chances are there's nothing wrong with it! If it hasn't been tuned in quite a while, it's likely to take more than one tuning before it holds pitch, so I'd encourage you to tune it up a few more times and see what happens.
Just so you know, the tuning pins are threaded like a screw, so tapping them in won't help if they are actually loose. But my guess is that the instrument is just adjusting to being under tension after so long and there will be a settling-in period where you'll have to tune it pretty frequently.