First, prayer of healing takes far too long to cast to use effectively in combat.
That out of the way, if you calculate CR as if all they're going to do is damage, then you're done. In combat healing is no more dangerous than dealing damage, so no adjustment is strictly necessary. It would be reasonable to calculate CR based on hit points after having cast false life, but that is fairly straightforward.
Finally, the CR calculation is an estimate, or starting point. If you try out this NPC and it is harder in reality than it was on paper, adjust the CR accordingly. Play testing should be the final determinant of CR, not math.
The first thing you need to do is figure out whether this problem needs to be resolved in-character or out-of-character. Is the warrior's player doing this because the player enjoys this kind of PvP activity? Or is he doing it because he thinks it's what his character would do?
If it's the latter, then you should take a look at My Guy Syndrome, then use the answers there to help you discuss the issue with the player. If it's the former, then you need to sit down with the player, away from the game, and ask him why he's so invested in attacking you. Explain that this isn't fun for you, and that you want to work with him to find a way to support his character's backstory without having to spend all your time unconscious and not participating in the game.
For example, in my current game, my character and another character don't get along (though the player and I are good friends). My character frequently "attacks" the other character, but those events are strictly roleplay - no dice are rolled and there's no in-game effect, just a fun interaction. Another possibility would be to have a third character get involved, someone the warrior respects. This third character could say to the warrior, "I know you hate mages, but we need the warlock to accomplish our goal. If you keep knocking them out in combat, you're putting the rest of us at risk." Roleplay solutions like these help the player feel like their backstory and RP choices are being respected, without negatively affecting other players' characters.
A few key points to keep in mind when having that discussion: RPGs are supposed to be fun for everyone involved, and the whole group is responsible for maintaining that fun. If this player's actions are preventing you from having fun, that's not fair to you (and potentially the other players, as one frustrated and upset player can often bring down the whole group's mood, however unintentionally).
Depending on the player's reaction to this discussion, you may need to get your DM involved. Talk to your DM privately (not with the warrior's player present, to avoid anyone getting ganged up on), and explain the situation and why it's frustrating to you. Ask the DM if they can do anything to mitigate the issue - perhaps to enforce these attacks as roleplay-only, or to help give a story reason for the warrior to stop attacking you.
TL;DR: Make sure My Guy Syndrome isn't the issue, then work with the player to find alternate ways to RP their character that don't negatively affect you.
Best Answer
Optional rule: Lingering Injury
There are no rules in the PHB limiting how often a PC can get up after being knocked to 0 HP. For DMs who don't like there being few consequences for dropping to 0 HP, in the DMG on page 272 there is an optional rule for lingering injuries that covers any PC who:
Experience with this rule
I've had two DMs use this rule, and each of them chose after a time to get rid of "receives a critical hit" triggering criteria. Why? Because the PC's receive many attack rolls against them; eventually everyone ends up with a lingering injury. All that the basic critical hit does in this edition is increase damage (HP reduction) done on that attack.
There are 9 choices, determined by a d20 roll. If you do the math a bit, as one of my DMs did, you realize that by level 11 everyone in the party will be wearing an eyepatch and be short of an eye, at the least, and will likely have multiple other performance inhibiting effects. And that's without having bad luck. You can be blind by level 3 with a little bad luck.
There is already a penalty at 0 HP: the unconscious condition
If enemies make attacks on unconscious PCs, it already causes two failed death saves, since the attack is automatically a critical hit if it is done by a creature within 5 feet.
When you are at 0 HP, a critical hit = two failed death saving throws.
Recommendation(if you want to apply this rule)
Apply this lingering injury effect after the battle if the PC dropped to 0 HP but wasn't killed outright, and / or missed a death saving throw by 5 or more. (Since you only roll those when you drop to 0 HP anyway, that is a supplement to the "drop to 0 HP" criterion). One of my DMs allowed the lingering injury to be alleviated by receipt of magical healing.
Thoughts on how to accept this game feature
"I feel like taking that kind of beating should mean something."
Is the problem that combat does not feel dangerous or deadly enough to your group?
Optional Rule: System Shock
In a related massive damage rule meant to emphasize "Combat is Dangerous and Lethal!" on DMG page 273, there is a system shock table that forces a Constitution save based on whether or not a PC took over half of their damage in one blow. This one penalizes PCs who do not pump Constitution, and those unlucky enough to be hit with a natural 20 roll by an enemy who then does double damage. If you apply this to monsters as well, to be fair, combat can change quite a bit.
I dropped this one after two sessions; it slowed combat down, and "stunned" (See Conditions, Appendix A) is a powerful condition (for the creature's opponents) to have applied to any creature. Most cases of stun require magic to apply, or require a Monk.