Nah; he's just a middle child so his crazy gets overlooked, just like the rest of his life.
Stannis is not what I would call particularly well adjusted.
He is
the most stubborn man in Westeros. See, some people exaggerate stubbornness as intractable during an argument or whatever, but Stannis takes the whole concept and applies it to every aspect of his life. I mean, I am just staring at the trainwreck that is the Baratheon Bros' life so far and I can just observe this stuff off the top of my head:
Robert:
1) Willing to drink himself into an early grave
despite and maybe especially because he has magic to heal the liver damage away.
2) Wants to treat a war with Viserys like the Trident Round 2 Electric Boogaloo, showing a tenuous grasp on reality for a guy who claims to have the same dream of crushing Rhaegar's chest in like a tin can every night.
2.1)
Viserys who would just turn him into a briquette if they ever fought from several hundred feet away. Or trap him in amber. Or into a turtle. Or crush with black tentacles... or literally a million better options than 1v1 melee.
3) Has a wife who is probably the biggest shrew and prideful lady in Westeros, publicly sleeps with someone who resembles her to taunt them anyway.
4) Punishes Stannis repeatedly (fail to capture kids? Dragonstone for you. Can't beat the Ironborn without losing a leg? A little public humiliation. Failed to capture or kill THE SAME KIDS?! Leaves you to rot in a prison cell. All for, what in hindsight, things that were never his fault. One
begins to wonder... At least until--
Stannis:
1) None of the above would have dissuaded Stannis from serving Robert loyally. It's like...
c'mon dude.
2) What it actually took to be convinced that abandoning Robert's cause was the right thing to do was someone being a decent person to him in all aspects of interaction, combined with being
literally the best person for the job. That implies Stannis' standards are probably as high as Viserys', and with a
lot less slack in the rope to climb there.
2.1) It implies that few people
actually treat Stannis decently. Probably because he always tells the truth, no matter how unpleasant it is to hear.
3)
Tells the truth when asked about why he failed, gets mocked and ignored, and continues doing even more risky things for the people who derided him. Because "am stubborn, must duty".
4) Would probably tell the Void, Abyss and Hell to fuck off if they tried to tempt him over to the dark side / despair, not even after thinking about it first, but reflexively because they thought they could get him to abandon his duty.
Literally everyone else would at least have to make a Will save.
Renly:
1) Takes a deal with fairies with godlike power because of a broken heart.
2) Is
actually surprised when the people he puts his trust in actually care more about their own ambitions more than him, even though they're unrepentant schemers who nearly starved him to death.
... I can't actually think of at least two more things for Renly yet, he hasn't been on screen much. I'm sure I'll find other ways to point out how very not well adjusted he is in the next dozen updates or so.