After further testing, it does appear that that plugin is causing some weirdness. It gets into endless buffering loops after a disconnect.
Thanks, Biff, for taking the time to perform some detailed testing. I figured that the rebuffering problem had to be due to something unique to my WinAmp settings, given that this problem was not reported elsewhere.
Of course, I want the best of both worlds (use their crossfader for music, but disable it for streaming media) so I will test tomorrow if unchecking the various crossfade options within the plug-in clears up the problem with the streaming feed.