I was just replacing my paper fixer and stop bath and was wondering: is the exhaustion of the fixer only due to silver saturation or does it go bad just sitting in the bottle or tray?
And then I started wondering about the stop bath also.
It's not a big deal, just wondering.
Back to a simpler answer for the OP

, because it is a big deal and there seems to be a lot of misunderstanding and misuse of fixer reported on the fora lately.
Stop baths are commonly either acetic acid or citric acid. The working solutions of these don't oxidize, but, as mentioned above, citric-acid stop baths will grow bacterial slime rather quickly and should be discarded after a short time. I mix mine "one session." Acetic-acid stops, like Kodak Indicator Stop Bath will last much longer. I've kept working strength KISB for some months with no ill-effects. Do, however, keep an eye out for bacterial growth, since, as reported, acetic-acid stops can grow this as well.
Fixers will go bad with time through exposure to air. A simple way to understand what happens is this: Fixer contains sodium sulfite, which acts as a preservative and keeps the pH correct. The sulfite oxidizes gradually. When enough has oxidized, the preservative effect goes away and the fixer "sulfurs out," i.e., begins to precipitate out sulfur in the form of flakes or granules. There is an accompanying rotten-egg smell. When this happens, regardless of how much the fixer has been used, you should discard it and mix new. (Regenerating fixer like Mr. Bill mentions above is not practical for low-volume users.)
So, we should not only keep track of throughput to determine fixer exhaustion, but also how old the fixer is and how it has been stored.
The lifespan of a fixer in this latter regard depends on how long and how much it has been exposed to air. Ilford's recommendations are in their tech sheet on Rapid Fixer here:
http://www.ilfordphoto.com/Webfiles/2006130218312091.pdf . The tech pub has a lot of useful info about fixers in general. I suggest reading it carefully. The relelvant info is below:
"Unreplenished ILFORD RAPID FIXER working
strength solutions should last for up to:-
6 months in full tightly capped bottles
2 months in a tank or dish/tray with a floating lid
1 month in a half full tightly capped bottle.
7 days in an open dish/tray."
Best,
Doremus