I recall a time when mine used to do that, though it doesn't now.
The only difference was that, a couple years back, I was using both .mp3 and .ogg titles in my gramophone folder. If I remember right, I'd read that .ogg was the preferred format, so I converted the .mp3's to .ogg and it hasn't skipped since.
I also only have about 30 tunes in my gramophone folder right now though, so that could have something to do with it.
Side Note - I've always thought it'd be cool to have the knob on the actual gramophone be a controllable volume control. As another small addition to immersion, if nothing else.