The reader never really knows if the old man is a real angel or if he is an old man who happens to have wings. The ambiguity seems to center on the duality of being an old man or an angel. Since we don't know what he is, we can only speculate as to why he survives.
Marquez blurs the lines between realism and fantasy. The result is a genre, which he helped develop and popularize, called "magical realism." In this story, we have an angel-like character who is described in very real human terms. We have a seemingly supernatural situation that is treated like a "familiar" situation.
If the old man is an angel, he is immortal and that is why he survives. But if he is an immortal angel, why does he appear old? And if he is a heavenly creature, why is he sick?
If the old man is just an old man, why does he have wings? If he is just an old man who happens to have wings by some genetic accident, why does he survive when his health begins to fail? There are no clear answers to these questions. Notice that the spectacle that takes the spotlight away from him, the spider woman, speaks clearly and provides a fable-like story about how she became a spider.
A spectacle like that, full of so much human truth and with such a fearful lesson, was bound to defeat without even trying that of a haughty angel who scarcely deigned to look at mortals.
But the old man speaks in an unintelligible language. No answers come from the man or the story itself. The reason he survives is anyone's guess; and that is the point of the story. It would be easy to give a story with a moral lesson; this is what the spider woman does. But the angel does not give such an easy lesson. He leaves it up to the people to decide what he is and how they should treat him. He does not help them understand and he does not intervene. Likewise, Marquez does not spell out a moral lesson in the story. He leaves it up to the reader to decide.