The company I currently work for had 3 offset presses each with their own storage area. When we initially prepare the plates for the first printing, we create a sleeve of heavy (14Pt or greater) paper that is sized to allow the plate and first piece samples to be inserted easily. These sleeves have our plate identification number on both sides down one edge. We also put a color coded year and month sticker on the same edge of the plate sleeve. When the job is completed, the pressman places the plate into the storage area in numerical order. If we haven't run a job in 3 years (as indicated by the year/month stickers) we recycle the plates. But if we re-run jobs, we update the year month stickers so we know that the job has been re-run and is current. To store the plates, the pressman is supposed to clean them thoroughly, rinse them thoroughly with water to remove the press wash/ink residue and then apply a gum arabic-water solution for preserving the plate and preventing oxidation. If the gum solution has to much gum, then it is hard to get the plate to take ink properly. But it really is the pressman's responsibility to insure that his stored materials are in proper condition.
One thing I have noticed though, once the plate is thrown out, about 50% of the time (at least with the company i work for) that old customer will re-order and then we have to remake the plate. Our boss wants us to throw out all of our old masking sheets (also stored by press type and numerically) that haven't been printed in the last three years. This is harder to do because sometimes, these old masking sheets are the only artwork we might have for a job.