Frequently, when the audio is out of sync with the video, it is because the person that created it used a very poor compression level (often for higher quality). This is why "homemade" videos are more often out-of-sync. I'd be willing to bet your PC is a bit old as well.

Stopping and restarting "fixes" the problem by buffering more of the audio.

You have a few options:

Make sure you have the latest codecs installed on your PC and that they are optimized for optimum performance (old codecs, while they can usually play the newer stuff, may take more time decoding).

If you are savvy enough, you can demux your video (spilt it into separate audio and video files) and recompile it with better codecs.

Make sure you are running the latest audio drivers for your sound card.

If possible, increase the size of the playback buffer of your media player.

Last resort, upgrade your PC.

More than likely, unless you are still running a 300MHz PC, a simple codec tweeking will solve your problems.