Short Version:
Maybe P is overwhelmed by bookkeeping and it's distracting him from situational awareness. Help him make a mechanically very simple character without fiddly bits or conditionals to keep track of, so he can focus on making good choices rather than having good bookkeeping. Invite the other players to support P with advice and by being good role models for the behaviour he's trying to cultivate.
Long form answer, with rambling and details.
Back in my very first RPG ever--and also my first time as a GM--I had a player whose poor choices got him repeatedly killed. Let's call him Q.
Q knew the rules and mechanics quite well, but had a very hard time applying them intelligently to whatever situation he found himself in (like forgetting to heal himself as a cleric). Even more than that, though, was his role-playing: he really really liked to role-play his characters, but that got him in trouble because when Q got deep into his character's internal motives the PC would lose common sense and perspective about the surrounding context of his actions.
It got bad. Really bad. Q's second character was killed by the party for betraying them (he had a conversation about his friends over tea with a "nice" lady). At that point I shared Making the Tough Decisions with the group. He studied it carefully, had intense discussions with me about it... and as a direct result his fourth character perished of untempered curiosity: the characterisation "very curious" overcame the common sense "half these items are cursed and my friends are begging me to stop," until the pile of treasure he was investigating yielded up a lethal curse.
After that session I took Q aside and we talked. He knew he had a problem, and he was trying to "get better," but he needed help. I'd noticed that all his PCs so far were mechanically complicated and required in-game bookkeeping: advanced casters and races with lots of conditional features and spell-like abilities to keep track of. So we hatched the simplest possible character build: nothing to keep track of. No "if you're flanking, X also happens," no spells, no per-day abilities. If his character sheet said he could do a thing, he could always do it.
We wound up with a kind of Indiana Jones flavoured skillmonkey (a rogue chassis with homebrew mods to replace things like sneak attack because tracking whether you can deal that extra damage was beyond what we wanted for the build). He wasn't optimised in the traditional sense--but since another PC in the party had straight levels in the NPC Expert class, that wasn't an issue in keeping him relevant in the group. Instead he was optimised for what Q needed: a simple no-bookkeeping character to let him focus on situational awareness and making good choices.
At the end of each session he'd hang back --along with any other players who wanted to-- and we'd reflect on the game: what worked, what didn't. We'd consult (and if necessary research) and come up with what to make sure we did again, and what we'd change next time. (I've since found that any game I run which has some form of this "reflect and plan" dynamic after every session is improved by it.)
In tandem with another player rising to the challenge and being a kind of "teach by example" role model, it worked. A year later Q was successfully running complicated wizard builds with great party dynamics and great depth of character. He was a real joy to work with, and all he needed was to wade in at the shallow end of the bookkeeping pool instead of jumping into the deepest part head-first.
nota bene: My players have tended to treat the group dynamic as one of table-level cooperation between friends. However much their characters may be rivals, at the table they collaborate to tell the best stories, and I'm also one of the collaborators. In groups where players and/or the GM act as rivals at the table level of things, I'm not sure how much my experience will be useful. It sounds like your whole group isn't really on the same page in terms of their desired gameplay experience, and communication isn't really strong. Working on improving the "friends at the table" level of things might help your game in a number of ways.
Best Answer
There are two components to building an encounter, I'm going to reiterate them even though you seem to have them, just so we make sure we're on the same page. These rules are laid out in the DM guide document of BD&D and should be much further expanded in the DMG.
CR only sets the maximum (not minimum, lower CR critters are designed to challenge in increasing numbers as you level) value for which a party should be facing. Generally you don't want to throw a CR 4 monster at L3 PCs (though you might on occasion if you want an especially deadly encounter).
the XP budget for the encounter type and number of characters is your primary source for building encounters, you take the appropriate budget number for each of your PCs and add them up (so for 4 L4 PCs that need a moderate challenge, your budget is 600). Make sure to factor multiples of the same monster as an adjustment to the XP budget (so if you wanted your PCs to fight a horde of goblins at 50 XP each, you'd need to factor that in. (you don't want them to fight 9 goblins, you want them to fight 4 or 5).
If you're doing those two things, WOTC thinks that you'll be balanced. However, this definitely does not mean your party will not wipe what supposed to be a hard fight easily and struggle with what's supposed to be an easy fight. In fact I expect them to.
The reality is that some encounters are simply a bad fit for your party composition, or a bad fit in general for that level of character. Other times encounters are an excellent fit and you've got an easy one on your hands.
The important thing, ultimately, is to learn the capabilities of your group and to identify the types of monsters and challenges that are hard for them and that they can overcome easily. This is obviously a lot more work than WOTC's advice on the subject. However, every group is different and it would be quite hard to give advice that works for everyone.