tennis balls, in a slinging application, should last until well after you lose them. they are designed to take alot of abuse, and they really aren't for distance throws etc being fairly...un-dense?...they won't go that far or that high due to the low density, so you don't have to worry about them depressurizing etc.
i can almost gaurantee that the slingers will wear out before the tennis balls, assuming you don't lose them all.
are you teaching them in some sort of sports feild or indoor gym, or just in a random clearing somewhere? it shouldn't be too hard to find most of them if you are somewhere with mowed grass...as long as the students don't throw too far...