Using Firefox shouldn't make a difference to the stream because once you launch Real Player from the link, it doesn't interact with Firefox at all (RP uses its own broswer to display our now playing information). I did have to click on the link a couple of times from Firefox before the stream loaded.
Also, when the stream drops out, try checking the quality of your connection. Go to www.broadbandreports.com
and click on tests and bandwidth test. This will tell you if something is hogging your network connection. You should get something close to at least 1MB download for a good cable connection. Real is also a processor hog so make sure you don't have too many programs running in the background. If you're running XP, click START, RUN, and type MSCONFIG. Click the STARTUP tab and uncheck anything that doesn't look like you're anti-virus program or anything else you use regularly. Also try running a spy-ware cleanup tool like SPYBOT. (Make sure to update Spybot after downloading and installing). Good luck!