He is tired, I wouldn't spend any time worrying about it especially because he is friendly still when talking about non-academic stuff. Its not worth dragging up why he isn't getting enough sleep because it could be a hundred reasons, and it is usually involuntary so we just let it slide it could just be a phase.
There is an advantage in everything though, and with this it can be a good opportunity to practice your presentation style or delivery with a safe audience, but with a sleeper in it so that you even have a tangible metric for your progress. See it like a challenge on what type of presentation will keep him awake, and note the times that he falls asleep and see if it is during the same part of the presenation.
LeaveShun details. Leave out all data points, statistics, process descriptions as possible. Counterintuitively, the less we say and the less we go in to detail about what we're working on the more others perceive us to be doing... that is, their imagination will fill in the blanks and if they ever do want to drill in to some statistics or details you will be able to effortlessly respond like a zen monk with all of the details you supressed earlier.
- Oh and one thing I want to add, and this may or may not be possible to do, but if he is responding well to talking about vacations and some non-math stuff like that, if you can somehow incorporate that into your presenation that may work... I don't know what your application is but if it could be talked about in the context of a vacation, just as an example here, then tying in some non-math content is maybe something to consider.