Do you have that problem when running in the Firefox SafeMode?
A troubleshooting mode.
1.You can open the Firefox 4.0 SafeMode by holidng the Shft key when you use the Firefox desktop or Start menu shortcut.
2. Or use the Help menu item, click on Restart with Add-ons Disabled... while Firefox is running.
To exit the Firefox Safe Mode, just close Firefox and wait a few seconds before using the Firefox shortcut to open it again.

If not, see this:
http://support.mozilla.com/en-US/kb/troubleshooting+extensions+and+themes

Does it work better you use File (or Firefox) > Exit Firefox instead of clicking the close X on the title bar?

I didn't try using File/Exit. The next time it happens, I'll try it.

Because the problem is intermittent, it would be hard to know whether starting in Safe Mode would help, unless I do it like that for maybe a week and see if the problem reoccurs.

Truth be known, even though I've used Firefox for years, it's performance over the last year or so has me very close to switching to Chrome or another browser. Version 3 often wouldn't start. I'd click on the icon and wait, and then click it a few more times, and afterward discover that as many instances of FF were shown in the Task Manager. Sometimes when I exited all of them from TM, it would start; sometimes not. And when it did start, it would often lock up. Now I see that v.4 has a problem with locking up. I don't think all the "improvements" have been helpful overall.

Thanks for responding.