Employee's performance is great, but attitude is on the floor

I have an employee who is, by all accounts, a great employee. If he puts his mind to it, he can consistently put out top metrics month over month, and when he doesn't put his mind to it, he's still performing at an above average level compared to most people in his position historically.

My problem with him definitely isn't his performance, it's his attitude. He's extremely negative, sighs and complains whenever he has to have a face-to-face interaction with a user, and, in general, just constantly has a dark cloud hanging over his head. I'm struggling with whether I should even say anything because it doesn't technically seem to be affecting his performance, but I'm concerned that a slow drip of this behavior is going to negatively impact the attitudes and/or the performance of the people around him. I can't speak to my other direct reports, but it's definitely impacting me and my general mood in the office.

How do I approach this without this inadvertently and causing impact to either his actual, documented performance, or cause him to want to quit? I've tried rewarding him, I've given him bonuses, and the maximum possible raise as allowed by an "exceeds expectations" rating for yearly reviews, I recognize him both publicly and privately, but none of it seems to be impacting his generally negative "aura" in the office. I'm also concerned it could just be problems in his personal life, which is understandable and, obviously out of my control, but after basically going on two years of this, I can only handle so much of it, seeing as I have to be around him 8-9 hours a day, 260 days of the year.

Edit: a detail I left out in response to a comment asking me to just talk to him and ask him what's up

I neglected to mention it in the post, but I've had this discussion with him once before, where I attempted to see if everything was okay with him, and be direct with my observations about his attitude, and tried to come from a positive place with a positive end. His walls were all the way up, and he became...

"Defensive" is too strong a word, but he wasn't as receptive as I would have liked him to been. I felt that it was a losing battle, I retreated, and things didn't really improve.