The trouble is, if you do reject him, he will probably never ask you again anyway. I wouldn't.
If I'm too tired to dance and the person asking me doesn't respect that, then maybe I wouldn't enjoy dancing with him as much as I thought... especially if I made it clear that I WOULD accept his invite if I weren't already totally pooped or hurting.
This is actually not a hypothetical for me... I recently at the end of a very long night tried to turn someone down that I normally enjoy dancing with (and had already danced with that night!) However, he needled me into another tanda, making it hard for me to refuse even after I said I was hurting. He wouldn't accept my refusal with graciousness. Now I have a whole lot less interest in dancing with him again, since he doesn't seem to care about my physical well-being or pain.
If you wouldn't ever ask someone again when they turn you down for a legitimate reason like being done for the night, then you are probably going to miss out on some great partners. Seriously? When someone tells you she is really tired or starting to hurt, you'll write her off if she won't dance with you anyway? Maybe you should try to ask her earlier in the evening next time!
If you see them dancing with someone else after they say that, well, that's different. But I've been approached on a number of occasions AFTER I've removed my shoes and even as I'm getting my stuff together and heading out the door. If someone won't ask me again in that case, I'll just assume their initial invite wasn't sincere, but they felt that they were obligated to ask me for some reason, so they deliberately waited until they knew I'd say "No". If you really want to dance with someone, wouldn't you maximize your chances of your invitation being accepted rather than refused?