Empathy should also apply to those who "have to" work with this young man. Yes, anything can be practice, but if I am practicing a martial art, I, for one, would certainly resent what I would see as a wasted hour - IF I had to practice with such a partner for the entire class. (On the other hand, if aikido is social work, then the worse the practice partner, the better for you - right?).
On the other hand, knowing how to work with a person who struggles like this young man struggles - on both a personal, psychological and a physical level could be a wonderful challenge. One of the ideals of any martial art is proportionate force - no more is necessary. So how do you NOT hurt such a training partner, as stiff as he is? How do you not hurt his feelings, by ignoring him, expressing impatience?
So - two suggestions.
1. Make sure you change partners on every technique. AND - you can make this even several times in a technique - for example, you do ikkyo for seven min - take a break to do some collective instruction, and change partners. Thereby, each only works with the young man for seven minutes. No big deal.
2. Have him work in a group of THREE. For obvious reasons.