My personal headcannon is that alicorns are immortal, but Cadance's immortality, unlike that of her aunts, works as a continual reincarnation cycle, which allows her to experience love with regular ponies during each of her individual lifetimes.
As for Celestia's...less than stellar combat record, I explain that as A) Nightmare Moon's power having been greatly enhanced by her transformation, B) Discord is simply too powerful for anything short of the Elements of Harmony, and C) Celestia held too much of her power back when fighting Chrysalis due to her being in the middle of Canterlot (i.e. Celestia's combat power comes in two settings; regular unicorn and dragon slave-esq destruction, with nothing inbetween).