Probably an Extension or/and Internet security software that block advertising or other unwanted content can cause that problem.

see : Error loading some websites

check : Configure firewalls so that Firefox can access the Internet

if does not solve it, start firefox in safe mode, select "Continue in Safe Mode" and see what happen.

thank you

If it were simply due to advertisement, I have to laugh as it happened when I clicked on the link to verify my email address when I registered for this site.

I have noticed that if I do a search, and click on a link for an advertisement, it does it. But it also does it when I'm trying to get to pages that I use all the time as well. I, too, have tried to erase history, cache, cookies, and changed it to no proxy. I noticed it started last fall and Firefox is the only browser I have problems with. Plus, it happens on both my computer and my daughter's computer with Firefox. I'm honestly believing that Mozilla has a bug or glitch that they just don't want to admit to as it would mean having to figure it out and fix it.

Such a "connection was reset" message isn't coming from Firefox, but from the web server or other servers in between the connection, including proxy servers and security software or malware that places itself in the connection chain.

Try to boot the computer in Windows Safe mode with network support (press F8 on the boot screen) as a test to see if that helps.