This is a tough one to answer for me because I just started drawing/writing "Whose World" recently (around Christmas of last year). So far, I've grown very fond of the characters I've created; although, they seemed to evolve and develop on their own with each strip.
On the other hand, I wrote a novel a few years ago and still haven't gotten over the fact that the story ended. I mean, I knew I'd have to end the story eventually--and I've been going back and forth about writing a sequel to it (but honestly, it doesn't need one.).
I think it all depends on how invested you are in the characters. Some are easier to let go than others--but you'll always leave a part of yourself behind when the time comes.
For now .. I don't plan on letting go of my current characters any time soon. I kind of want to grow old with them. 