You've got an interesting idea there at least. A shield system that gets stronger the more you shoot at it. How annoying for people shooting at you.
Technically, the shields don't need more power to become stronger; apparently they need more power to REMAIN strong when they've been strained and overloaded. Possibly they need more power to coolant systems that keep the field generators from overheating, but the result is still that they can only take so much punishment before you can't put enough power into them to keep them intact.
Regenerative shields wouldn't route that power back into the shield generators, but probably back to whatever system needed them.