I like the concept, but as has been mentioned, it is prone to someone having a string of bad dice rolls and not getting to use any cool abilities after their first round. I might have the required roll result tick down each round - so the first round you try to recover you need to roll a 4, but if you fail, the next round you only need to roll a 3, then a 2, and then on the following round you automatically re-prime your abilities.
EDIT: That would allow you to introduce really powerful abilities with an automatically delayed recovery rate, by giving them only a d3 recovery die. So you definitely won't recover the next round, but you might do so the following round.