FF isn't that unstable & should not keep crashing, I run a derivative of FF 9.01 - Pale Moon & in weeks of running it I can't remember it ever crashing.
The fact that IE does the same thing would seem to point to issues in your install. Have you run a scan with the free version of Malwarebytes Malwarebytes Site on checking others PC's I often find this anti-malware program often finds problems that eludes other AV's.
Right OK will switch to FF10 Beta 5 as Firefox 9.01 still going through fading misty screen saying "Firefox is not responding".
Maybe it's one of my addons but then it wouldn't happen with I.E. as well, alternatively I might have too many windows open.
Can't possibly be a bug as all zappers have been run , Malwarebytes, SAS etc in addition to Windows7 security essentials and checked with ASC. All show nil result apart from Ad cookies which are deleted regularly.