This is really a difficult question to answer and will vary battery to battery. We can't provide a specific shelf life for the batteries but they will actually last longer if they are used periodically. Lithium batteries degrade slowly over time, even without use, and if they are left all the way at zero there is a decent chance they will not be able to be charged again. As long as they have a good charge on them prior to being stored and they are stored in a cool, not cold, location they should last a couple of years, or possibly longer, and still work and be OK, but it is not recommended. The exact length of storage time allowable is an estimate.
A suggestion would be to actually rotate the batteries with ones in units every term/semester/six months and store them with a good charge, doesn't need to be completely full, when not in use. Or at least take them out periodically, put a couple of hours use on them, charge them again and put them back into storage. A better suggestion would be to buy the spare batteries in a year or two so that they are not stored as long. And even better would be to wait until it is noticed that the batteries in the units are not holding a charge as long and buy replacements at that time.