It at most forces one save per turn.
If the creature remains in the greased area, then it might have to save again if it is not already prone. But if it starts its turn in the grease (prone or not) and then exits, it is still difficult terrain. So you want to make sure the enemies will be forced to cross the grease, or at least can't just exit by moving closer to you.
When the grease appears, each creature standing in its area must succeed on a Dexterity saving throw or fall prone. A creature that enters the area or ends its turn there must also succeed on a Dexterity saving throw or fall prone.
So the only moments a creature must make a save are:
- When the grease appears
- When the creature enters the area
- When the creature ends its turn in the area
However, you are interpreting the spell wrong.
It is not a spell meant to keep people prone. It is a battlefield control spell. Need to cover the party retreat? Grease the tunnel behind the last person. Want to make the enemies take longer to get to melee range? Grease between you and them.
Enemies will lose 20ft of movement to cross the greased area in the best scenario (for the enemies).
Also notice it does not use up concentration, and this is a big plus.
There is this video by nerdarchy about using the spell. Except they got it wrong in the first segment. Grease is not flammable. And they got the burning hands spell damage wrong.