Sleeping late

Now might be a good time to introduce a companion to walk with him around the block and to do appropriate exercises in the home even chair exercises. Stretching and balance exercises are good. He needs to be mobile and ambulatory for as long as possible. Read a few articles on fall prevention for older adults, they talk about exercises. As your PCP if home PT can be ordered. Ask for a balance evaluation. Medicare can pay for this.

Iris

Iris is right that if you can keep him mobile, it will certainly help. But what you're seeing is probably a combination of things you can't reverse: a lot of PWD sleep more as they progress, and he obviously doesn't have the executive function to either get himself to the gym or to know what to do with himself when he got there. It might work if you went with him—but then that eats up your day, too. I personally would let him sleep in so that you have your time, and just keep an eye on keeping him as active as you can when he is up. If you could get him to accept a home companion (even it's in the afternoons), well and good.