For what it is worth, I've had the same trouble with all versions of Debian and FF for a "while" now, and have spent time trying to investigate it off and on during that time.
A "while" is possibly a couple of years? I didn't have any desktop computer for a while, and when I did set one up, I ended up using WiFi instead of hard-wired, which is when I originally noticed it. So, I can't identify when it started happening. And I'm not currently able to check to see if this would go away when hard-wired. For me, the biggest signal is GMail and similar apps will go into a "You are not online" state. I've done a variety of tests, such as having ping running in a shell, using the browser console to catch certain events or polling values like navigator.onLine. I've dug through FF about:config items looking for what affects this so that I could control it, but not yet any luck. I've gone through most, if not all, config settings exposed via XFCE's settings (e.g., Power Manager), as well as Network Manager. Again, no luck. I've tried running an instance of FF under separate X sessions (Xvnc, Xnest, Xephyr, Xpra), with no luck. Probably the only thing I haven't tried is a full fledged VM. I've done a lot of web searches which have mostly led to folks mentioning the same issue, but no real solution. For me anyway, the time between the screen-saver kicking in and GMail going offline is long enough that I get distracted and forget that I was running a test. So tweak-setting/test cycles are difficult to do. All of this is just to say, OP is not alone in dealing with this issue. Yes, it is restricted to Debian (I've seen the same problem at least mentioned for MS-Windows). Yes, it is *likely* restricted to Firefox. But, asking on a Debian list might find someone who has had an "Aha!" moment. mrc
