Realistically, to me, shields should be regenerating whenever they're not taking fire. I think there needs to be special a reason why it is called 'regenerative' shielding.
That said, I like the idea that regenerative shields somehow absorb incoming energy for use. I don't like this as being redistributable to other systems, though.
The way shields were depicted in 'Equinox' might be worth studying, or might only complicate things. I seem to remember the crew somehow managing to reinforce keep the shields up even after the generator was stolen, using the nav deflector? Perhaps then regenerative shields tie the nav deflector into the shield system to absorb the energy expended against them.
Well, first things first... the term is simply a made-up term, invented by people working on a TV show with barely even a high-school science education. So all it "really" means is "gee, we've heard this neato term being tossed around and so let's use it to sound super-keen!"
The term, of course, is used primarily in regards to a braking system used on electromotive vehicles (electric or hybrid). The idea is that instead of dissipating motive energy as heat (like normal brakes do) you use it to drive a very stiff "generator," converting it into AC electrical power (which can then be rectified to DC and pushed back into energy storage cells).
The point of "regenerative braking" is to avoid wasting energy, and instead to recapture energy which otherwise would be lost, for future system-wide use.
Since that's the point of the term in real life, and since the writers were (without fully understanding the term) emulating this real-life concept, I think we should apply the same concept.
That is... energy which would otherwise be wasted and dissipated is instead reclaimed, absorbed if you will, and redirected into the energy storage system.
Of course, the shields themselves are an "energy storage system" of sorts (as I mentioned earlier) so it could be that the energy is redirected into them, or it could be that it's redirected into the ship's batteries and capacitor banks and so forth.
But, of course, in reality.. it's just nifty technobabble.