I'm not 100% sure of this, so please do additional research. From what I've heard, not every software company does it the same way. I've never heard of programs that only allow one install, but they might be out there.
But some academic versions won't allow upgrades (i.e. if you buy a new version that looks for an older version already installed, it won't recognize the academic version and won't install). Others might have reduced functionality. Some programs aren't discounted very much, others are discounted a ton.
Your best bet is to do a search on academic software and then ask the dealer what the specific restrictions are on the software you're interested in. You'll probably need to provide a copy of a current school ID in order to qualify for the special price. But frankly, if you can save 75% by giving up the ability to buy an upgrade version in the future, who cares. You might get years of use out of it.