This has been talked about since someone first thought that Twilight could become an Alicorn. A character that's defined by friendship, gradually looses all of her friends. The same thing can be said for Cadance, a character that's defined by love outlives the love of her life. This makes for good speculation and fan fiction, but its not something the show would ever cover. However, people have bugged asked the show's writers about this issue. This is how Meghan McCarthy responded.

http://www.equestriadaily.com/2013/04/twilight-sparkle-wont-outlive-her.html

Its possible that Celestia and Luna are the only immortal alicorns, and any others will have a normal lifespan. But again, this is all speculation, as we'll never actually know.

I'm not convinced it's as bad as it sounds. Yes, Twilight will likely continue to live while the friends of hers that we have come to know will pass on, but the thing is she will make new friends. And they will pass on, and more friendships will be formed, etc. So, to say that all of Twilight's friends will pass on is not to say that she will lose all her friends, and I could easily see the gains making the losses bearable.

I have lived through the deaths of several beloved, pet cats. Unless something goes catastrophically wrong, I will live through the death of at least one more, likely several. Maybe I'm being presumptuous in comparing the two cases, but I've found that the companionship provided to me and the good I can do for them generally outweighs the knowledge that I will have to watch their last moments, painful as they may be.

I see you point there Ravener, and I read the post on the forum Carsair, valid points, all of them.

However, the forum made me think. What defines an immortal alicorn? Is Twilight immoral or not? If not, is it because she became an alicorn and not born one like Celetsia and Luna?

I'm actually going to post theory #2 very soon on the "What if she is indeed immortal."