If your institution has a records-retention policy, it may address the issue.  Ours does not require us to retain UNFUNDED proposals longer than one year; however, as others have mentioned, as soon as you dispose of one, someone requests a copy the very next day!  And, of course, federal agencies--and perhaps others-- occasionally fund a proposal that was submitted more than a year earlier.

Some issues to be considered are space (of course), access (if you put them in storage, are they truly accessible or might you just as well toss them?), disposal (do you return to the faculty member who may or may not have a copy, do you shred them?), cost (what is the cost of storage space and/or disposal?), and what likelihood is there (apart from Murphy's law) that you'll need them longer than whatever period you decide upon for retention?

Hope this is helpful.