Yes, the PC protected by Sentinel at Death's Door will take a single death saving throw failure
It's pretty straightforward if we look at all the pieces in sequence, and most of the citations are already in the question.
A creature at 0 hit points is, generally, subject to the Unconscious condition, which transforms any hit into a critical as long as the attacker is within 5 feet:
Any attack that hits the creature is a critical hit if the attacker is within 5 feet of the creature. (PHB, Appendix A: Conditions, Unconscious)
When it applies, the Sentinel at Death's Door feature transforms a critical hit into a normal hit:
As a reaction when you or an ally that you can see within 30 feet of you suffers a critical hit, you can turn that attack into a normal hit. Any effects triggered by a critical hit are canceled. (Xanathar's Guide to Everything, Chapter 1: Subclasses, Cleric, Grave Domain, Grave Domain Features)
So a critical hit becomes a normal hit when this feature is activated. The remaining question is what happens on a regular hit to a creature at 0 HP:
If you take any damage while you have 0 hit points, you suffer a death saving throw failure. If the damage is from a critical hit, you suffer two failures instead. If the damage equals or exceeds your hit point maximum, you suffer instant death. (PHB, Chapter 9: Combat, Damage and Healing, Dropping to 0 Hit Points, Death Saving Throws, Damage at 0 Hit Points)
So in summary:
- The two death saving throw failures are a result of the creature at 0
HP taking a critical hit, but only one failure would be imposed on a
non-critical hit
- A critical hit is automatic (under some circumstances) for an
unconscious creature target, but this class feature converts a
critical hit to a normal hit
- And so if the feature is used then the critical hit becomes a normal
hit, and the creature at 0 HP suffers the effects of the normal hit
- That effect is a single, automatic failure on a death saving throw
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