If you can't grow old at all, what would you then do with your life? And at the end of the movie, adaline is dem happy to see a white hair... something most of us would dread. With all the hardship and difficulties in life, maybe it's not such a good thing to live forever.
This also reminds me of another movie, which the family had the ability to go back and forth in time, by entering a dark space or a cupboard. So you can go back and switch things you'd have regretted doing. But given the opportunity, would you? It might not make a difference, or it might be just too cumbersome after a while, to go back and change everything, everytime something goes wrong.