Here's something odder...
I've found that hi-bitrate streams work great. 96, 128, 160, 192 kbps all work wonderful. The station I listened to that caused me the most havoc was from rangerplex.com (can't post direct link to station due to RIAA legalities and LoudCity), they recently upgraded to a higher bitrate (96 or 128 depending on the show), up from 24 kbps.
Also, I've found that when I SSH into my box here at home, when stuff is idle, the connection seems to drop.
I believe it boils down to a TCP timeout issue, too short specifically. 24kbit isn't enough to keep the TCP timeout from kicking in periodically. Maybe a rooted droid could be used to change the TCP timeout, and see if that helps any?