This question regarding monks' Timeless body feature recalled to me the similar phrasing of the Oath of the Ancients paladin's Undying Sentinel feature (Player's Handbook p87):
Undying Sentinel ...Additionally, you suffer none of the drawbacks of old age, and you can’t be aged magically.
Contrast to the monk's Timeless Body (p79):
...your ki sustains you so that you suffer none of the frailty of old age, and you can't be aged magically. You can still die of old age, however...
Unlike the monk's feature, there's no mention of dying of old age in the paladin's feature. So, can a high level Oath of the Ancients paladin die of old age?