Sounds really weird.
I would try the usual steps:
- Check your hard drive for errors (with Disk Utility)
- Repair permissions (with Disk Utility)
- Run Apple Hardware Test (included on the system DVDs that shipped with your Mac)
If no problems are detected, try a clean installation of Snow Leopard, install all the updates (but no 3rd-party software yet!) and see if the problem still persists.
But before you do anything: Make sure you have a complete backup of your data somewhere.
I'm running disk utility as I type this. I will post again once that's completed.
I do not have system DVD's as the iMac was purchased used.
I absolutely do not want to do a wipe and install of the OS because it took me two days to install all of my software and I don't have that kind of time. I'm booked well into September and down time is out of the question.
I have never seen a Mac quit applications by itself. Could you explain more? For example, does the Application's indicator light on the Dock actually turn off (this would indicate Quitting)?
If the problem persists, I would backup all your files & do a clean restore on OS X (install the Snow Leopard Disk, restart, Erase the Macintosh HD, and install OS X).
It quits everything and will completely log out if something does not need saved and stops it. I've never timed it, but I bet it's less then 10 minutes of idling and then it does it.
I'm also having a lot of problems with my FireFox browser. I have to force quit it 1-3 times a day because I get the rainbow spinning ball of doom for extended periods of time.
Sorry I can't help diagnose the problem but have you tried downloading caffeine to keep the system from idling?
No I have not, but I will certainly look for it and try it out.