This sounds like a memory leak, though the symptoms of the machine getting worse and staying worse once the AIR app is closed is pretty odd.
Which version of AIR are you using?
Is there any 'downtime' when these presentation machines could reboot?
Ive run a test version and checked the memory usage using some open source monitors like the one described above (high res stats). Im no expert with trying to test for memory leaks, but this does give feedback to direct, max direct, total and garbage. After running this air app for a few days the memory remains stable. On my test screen the direct and max direct are around 30 and 45 (i assume its MB).
Theres an image attached with these monitors - this picture is taken with me testing the movie in the flash ide so i believe thats making these values much higher, however they also are remaining stable.
I think the version of air used initially was 2.5 (this is the one thats misbehaving), i've since loaded version 3.1 into my copy of flash CS5.5, i need to run a long test with this version too. The trouble is that problems seem to take weeks to appear. I will be setting up the final version of this mac mini setup to restart automatically every night.
I'm currently testing a version of this film as a flash projector rather than air to see what that does. Please let me know what other tests i can run. I can post the code i'm using - its not that big (200 or so lines)
To explain a bit more about what i'm doing - I work for an artist who makes dynamic (randomised) animations which play on HD screens using Macs and PCs. These will generally be left on all day, some are never turned off, some are. I've seen a few different films recently freeze (fine when its quit and restarted) or in this case slow down to almost 1 frame every 30 seconds and completely break the computer, in some cases requiring the system to be re-installed (the film i'm talking about falls into the latter situation).
Just a quick note about the machine getting worse - the mac mini this is running on is only running this air file and nothing else - once the machine went wrong we swapped out the mac mini and put the same film on a new one. That also now has failed and wont restart in the same way.
The original mac i reinstalled the system and it seems fine now. I'm going to visit the client and get hold of the newer mac mini and see whats going on with that - hopefully i'll be able to access the hard disk and send/post any error files if there are some.
That definitely sounds odd. Not only is something leaking, but the system is corrupted too? That's not normal.
We do have some longevity testing with Flash Player and AIR on desktop machines of various sorts that run for at least a week at a time. We're not having to reformat our systems.