From my own point of view, losing an appendage means it wasn't worth the space. Yes, I could go through the process of fixing it or forming an exact duplicate, but all-in-all, it was just far more convenient to just get an entirely new limb instead, one that is harder to remove or more useful. Take a bad situation and turn it into a good one.
Anything vital, such as my torso, head, etc. regenerate almost instantly unless a specific kind of energy is used to damage it. Anything not so vital, such as legs, don't really grow back at all unless I want them to, and it is not nearly as fast because it's not nearly as important.
But this is all based on my "what-if" scenarios to get an answer.
If you want one that has more basis to it, then here it is :
A creature with a humanoid-esque form tried to possess me, and in so doing lost his left side from the side of his neck down in a diagonal shape almost to his hip. In all the instances I have seen of him after that experience, his energy level is much, much lower than it was when he was "complete" and what was taken from him is still absent from his body.
So it probably also depends on just what kind of being you are talking about here. Some seem to be able to do it naturally, and some seem unable to do it at all.