I'm not sure which dialog that is; maybe it's something new that I haven't seen in Windows 7. Next time it happens, could you capture a screen shot of the dialog? This article has tips on that: How do I create a screenshot of my problem?

Meanwhile, can you see whether Firefox is recording crash data? When Firefox crashes, it usually records information about what was happening at that moment. You can submit that data to Mozilla and share it with forum volunteers to see whether it points to the solution. Please check the support article "Firefox Crashes" (especially the last section) for steps to get those crash IDs, and then post some of the recent ones here.

Have you noticed any patterns about what sites or what kinds of content were open in Firefox at the time it stopped responding?

There is no crash. The Firefox simply freezes, no more response, no notification other than a pop up window that says Firefox is already running and I should pen another window (?) and/or restart my computer. Sorry, I did not take a screen shot of that window.

You can kill the Firefox process in the Task Manager in such a case.

See:

• "Hang at exit": http://kb.mozillazine.org/Firefox_hangs
• "Firefox hangs when you quit it": https://support.mozilla.org/kb/Firefox+hangs