You DID learn the spell so that you can use it infinitely. Your infinite use just happens to be limited by the amount of MP you have. MP in this game is dividied into tiers. Instead of having general MP that go toward any spell, you have a designated number of uses of any spell on that tier. So instead of having to do the calculations to figure out how many times you'll be able to use a spell, you can just look at the number. The number of MP you have per tier increases as you level up. When you cast a spell, you use one MP from that tier. MP can not be re-allocted. When you're out of MP in that tier, no more spells from that tier. In order to regain MP you must rest in an INN or a CABIN. This is actually not unlike the rest of the FF series, only this game was made before ethers had been dreamed up.

P.S. when posting in a forum about multiple games, it is helpful to specify which of those games you're talking about.