Funny I had a similar problem this week ended up reinstalling it. I think it may have been an add/on issue. If you click start> Programs now look for the Mozilla Firefox Icon left click on it once you will see the option for (Safe Mode) you could try doubling clicking the safe mode option and see if firefox connections work better. Running in the Safe Mode, not to be confused with Windows Safe Mode disables the add/ons in Firefox. Good luck and let us know.

This sounds like your problem: Here is a link that might be useful: Forum

DA said "All-in-all they are so much the same. FF has seemed to have lost some consumer confidence ever since it went to the rapid rate release development a couple of years ago." Agree, agree. Maybe Firefox has lost some QC in the process? I was having random stability problems with Firefox, including whole machine freeze-ups, odd behavior, crashes. Different machines with different users and not all the same Win versions. I deleted Firefox, put Chrome in a prominent position, and all is well. I had no compelling reason to keep it and have found with regular use I like Chrome better. Everyone has a different experience. Android-wise, I just use whatever was bundled with it, it seems fine. I always try to use purpose-built apps more than the browser anyway.

Keeping up with all the updates with a dial-up connection must be a nightmare. Windows, web browser, antimalware, antivirus, it never ends. I have slow "out in the country" DSL and have turned off most automatic updates.