Eric-

At PowerDNN we sometimes encounter situations where a rogue piece of code causes the site to use exhorbident amounts of virtual memory (however I wouldn't consider 500 mg much of a problem) and we typically get a hold of the customer and alert them to the problem.  Sometimes in a situation like this, the lack of RAM due to resource over consumption compells us to cap the affending customers RAM at 250-500mb.  I have actually seen RAM capping in IIS, cause an application to start and shutdown in the same way you describe.

I definitely agree with Mitch and Sebastian, you should deifnitely be upgrading the site.  On top of their being major performance enhancements, their are some extremely critical security patches.