I don't think there's anything in ABC2Win to disable the player after a certain time - the only limitation is on printing scores if you're not registered. And hell, registration is only $20.
PLAYQABC is a DOS program which only uses the beeper, not your sound card, so I would suggest that it's probably a DOS problem.
I find PLAYQABC OK for just checking tunes, but usually play them through ABCMIDI, where you can change timing, instrumentation, etc, and play the full sequence, not just the parts. I think I found the download for that (is it ABC Midifier?) on the ABC homepage, which you should find a link to somewhere in Mudcat