When I first got my female betta she had some damage to her fins, and they were completely healed within a week. Whereas my older male has had damaged fins for over a year and once he was finally distracted from tail biting, it took a couple of months before they grew back. So age probably has a factor, as would how often and for how long the damage has been occurring.
Remember that the tank your fish lives in is his or her's whole world. Ask yourself this question, and answer it honestly: would you choose to live there?