Should you ever give up on someone?

There is an older gentlemen at one of the dojos I attend. He is maybe 65 years old (although it is sometimes hard to tell with Japanese people!) and I don't think he has ever studied any other martial arts very seriously. He may have done some kendo when he was younger.
He's a very kind, friendly, and genial man. He attends classes quite regularly, and seems to be trying his best. But the problem is, he just doesn't "get it".
Now, I don't expect everyone to be a martial arts genius. God knows that I am on the low end of the "athletic aptitude" scale - I can't dance, can't really swim, am hopeless at ball sports - and I'm not even very good at martial arts when I consider how long I've been doing them.
But this older fellow, I'm sorry to say, has real problems with co-ordination. Sensei, or a senior student, will show him a simple movement, such as stepping forward and cutting, but he will transform it into something quite different. It is very common for Sensei to lose his patience with him. "Your right foot! RIGHT foot forward! That's your left foot! I said your right foot!" "Ahh," the old fellow will chuckle with some embarrassment, and blink a few times, and then change his footing. This makes Sensei even angrier. "Don't say 'Ahh' all the time, just remember it and do it properly!"
I haven't practiced with him very often since he joined the dojo last year. The other day, though, we were doing a partner rotation. I got to the end of the line, and rotated down to the beginner end of the dojo where he was waiting. I was on the jo side, he was on tachi. He came in, but none of his attacks were even close to reaching me, so I just stood there, hoping that he would pick up the hint that he needed to get closer. He didn't, he was just confused because he couldn't think of what he should be doing next. I explained, and we tried it again. Numerous other problems surfaced. For one thing, I found myself getting annoyed because he wasn't even walking back to his original position at the end of the kata, but rather going back on a diagonal and ending up shifted 2 or 3 meters to the side. I started to wonder whether he has some serious spatial perception issues, or issues with balance, or some other problems. It really came to a head when we did a kata that involves the swordsman coming in for a cut, and the jo side moving into close range and blocking/jamming up the swordsman so he can't cut. We did the technique, but instead of moving back to take the second cut as he is supposed to do, he just leaned around to the side and slowly twisted his arms, kind of bopping me in the shoulder. It didn't hurt, but I wanted to ask him, "What the hell are you doing?"
I say again that he is a really nice guy, who seems sincere in his desire to learn. I was getting annoyed in spite of myself, because I was really trying to be patient. But he does seem to be the "perfect storm" of bad characteristics for a martial artist - a poor memory for techniques, an inability to perceive what Sensei is trying to teach, a low awareness of space, and a very poor awareness of what his own body is doing.
So, what do you think? Should some people just be encouraged to take up bird watching? Weapons kata are not usually very dangerous, but I'm not crazy about the idea of training with somebody who often does the totally unexpected, or without any control of his motions.
I imagine that, somewhere down the line, he will quit. Sensei will stop teaching him, if he doesn't manage to internalize any of the corrections he's been given. Or, he will try a grading and fail, and then fail again. Or (and I hope this never happens) he will hurt somebody, and be so embarrassed that he will stop coming to practice.