538 did a piece on this. Basically Rogers is always conservative to avoid the interception, even when a risk is needed to win the game.
Skeptical Football: The Aaron Rodgers Enigma
I don't know if all that is right, but it's an interesting perspective that seems to make sense. And it is odd that he has so few comebacks given how good he is normally. Been down 21 times by nine points, never pulled out a win.
Rodgers is basically the anti-Stafford. Neither changes their approach based on game situation- Stafford remains a high-risk gunslinger, whether you're down 14 in the 4th or up 14 in the 4th. As a result, your win probability with him doesn't change nearly as much based on point differential at the end of the game as it should, in either direction.
Rodgers is the opposite: he stays conservative, which pretty much preserves whatever outcome you were trending toward. If the Packers are winning at the start of the fourth quarter , they'll win. If they were losing, they'll lose. Either way, he's not going to change the outcome. And it's not just fourth quarter - Rodgers' record is really bad (compared to the other elites) in games where his team has fallen behind by 7+
at any point. He's a front-runner, and I don't say that in a derogatory way necessarily. That was Tiger Woods' MO back when he was good as well, and it always suited him fine. Rodgers is at his best when he basically ends the game
before the fourth quarter. Which he does often, and that's what the Packers optimize their defense to excel at.
Rodgers is just a different kind of QB than Brady. He's more likely to blow a game open early, and he does that by combining deep downfield throws and interception avoidance in a way that nobody else really does. He deserves all the accolades he gets for that. But if it's close late, or if god forbid you actually have to make a comeback, he's not your guy. Never has been, probably never will be.
When it comes to maximizing win probability at all point differentials, Brady and Manning are in a league of their own. Last year, I saw a great article that included curves plotting how the various QBs' win probabilities tracked with point differential in the fourth quarter. Can't seem to find it right now, but I'll keep looking. It was really interesting, and relevant here.