Regeneration depends on the fin rays..sometimes if the main dorsal (top) is damaged too badly or the pecs(little side flappers) the fish will tire and die.
the caudal and anal (tail and skirt) naturally tear off long fin specimins all the time.
No biggie, though sometimes they come back like an ugly ragged crown with scarring (clear or white skin) on the edge.
I'd be more worried on if the body got compressed or the swim bladder damaged.
Only time will tell. Bettamax is a good product but overused (the blue soup most pet store bettas is in is bettamax). Fin damge is usually best combatted with daily water changes as long as there is no infection. We use asian almond or bannana leaf because we bought it to have onhand.
Good luck witgh the little guy. My son almost fed his bettas to death once. But I made him do an immediate tank change and look at his gasping fish. He has been very sparing since.
He takes good care of his friends now because mean old mommy used the "do this? and your fish will DIIIIE!" lecture, "you don't want to kill your fishies do you?" My son is 5 though. Three is a harder sell!
good luck..best to put Mr. betta atop a dresser or bookshelf about 3 ft up.
Heh Alli! We all are making betta beds now. :P Crxi found a better way (fake plants) than mine (live that die a lot). And the bettas looove it!
Mine now has a Repti water dish leaf double boiled and soaked in Kent. 8)
Least til I find some java fern. the riccia explodes adn so does foxtail and hornwort. My watercress didn't have enough current.