Greek gods are not deathless by nature in the way a philosopher would want. They are deathless because of what they consume, and Homer says so plainly: they do not eat bread and do not drink wine, and so they are bloodless and are called immortal. Ambrosia and nectar are the substitute diet, and the pair is the mechanism by which divinity is maintained rather than a reward that follows from it.
The usual division makes ambrosia the food and nectar the drink, and that holds most of the time. It does not hold always. The poets occasionally reverse them or use one where the other is expected, and the inconsistency is old enough that ancient commentators noticed it. What no source ever supplies is an ingredient. Neither substance is described in terms of anything it is made from, where it comes from, or who prepares it, and this is unusual for Greek myth, which is normally happy to explain the origin of a thing.
Ambrosia has a second life outside eating. It is an unguent, rubbed into skin and hair, and Hera uses it when preparing to deceive Zeus. It also preserves: Thetis drips ambrosia and nectar into the body of Patroclus so that it will not decay while Achilles delays the funeral, and the same power is used elsewhere to keep a corpse fresh. The unifying idea is not nutrition but incorruptibility. Whatever the substance touches stops being subject to time, whether that is a god who eats it or a dead man who is anointed with it.
Given to a mortal, it works. Feeding ambrosia to a child is part of how a goddess sets about making that child immortal, and the attempts that fail in the stories fail because they are interrupted, not because the substance is inadequate.