The thiosulfate in fixer does break down due to oxidation over time, but it does not happen nearly as quickly as it does to developers. When it does start breaking down, you will know it. I have a gallon of Kodak powdered hardening fixer mixed up and ready to go now for almost 6 months and it is still ok. The last batch was well over a year old and there was only about 1L left in a partially full container before it started to go bad. On another occassion, I had a small amount of rapid fixer concentrate in a bottle, again over 1 year opened, when it started to degrade. Sulfur precipitates out, making the mixture cloudy with coloidal sulfur in suspension and giving it a distinctly sulfurous smell. If the fixer is not too far gone, it will still clear a piece of undeveloped film and you can still use it. I would not use it for fixing film or any important prints. It will be fine for test strips, work prints, etc., in short anything where permanence is not required.
In use, fixer deteriorates because of several factors. Residual developer carried over into the fixing bath is one reason, but this effect is largely nullified with the use of an acid stop bath in the case of acidic fixers. I minimize the carry over by rinsing my films with clear water after the acid stop. Papers can be treated the same way if you have some running water in the darkroom. I don't, so a quick dip in a tray of water that gets changed every so often suffices. For the most part, the fixer simply gets used up while doing what it is supposed to do. Undeveloped silver halides are converted into water soluble compounds which are then carried away by the water in the fixer. It is precisely this reason why undiluted rapid fixer concentrates don't "fix" anything. There is simply not enough water to carry about the byproducts of the fixing process.
