That is a weirdass issue, most likely not caused by FF7Music, but by Winamp's waveout plugin. You sure you don't have any other audio software running, custom drivers, etc? Things like "SRS HD Audio Lab" or other sound enhancers not included with your soundcard can cause all kinds of trouble. It could even be an alarm app or something that doesn't manage the sound driver nicely.
I can't imagine why it would do this so suddenly after as long as half an hour or so, it's certainly not an issue I've encountered. You say you're using the latest installer? You think you could post a screenshot of your ff7config's audio tab, as well as one of Waveout's settings (in FF7Music, click Configure, make sure out_wave.dll is selected as your output plugin, and click the lower configure button on this screen).