IŽd like to add my 2 cents here. Firstly: Yes, it is possible that the wish to play goes away during stressful times.

As for me, the more stress I experience (outside the relationship), the more desperate I get for play. It centers me, relaxes me, I can let go of everything, and afterwards, I have my mind free to go about solving the problem or just have more endurance to stand through a difficult time. I am the sub, though.

With my husband (he is my Dom), it is the other way round - if he experiences severe stress, he does not have any will to play.

I found this applies to all couples I know - even if it is the other way round sometimes (the sub not willing to play during stress times, while the dom would like to).

So in my opinion this is nothing to worry about. I do not believe he is lying to you. It might well be he actually functions that way. In this case, I think forcing him into play would be a really bad idea and might do damage to your relationship.
As for the suggestion to kick him out of your life for being that way - I would be careful with that. Me and my friends are otherwise very happy in our relationships and would not kick a good partner into the rubbish bin just because he functions differently.
A bit patience is needed here. But usually - unless the problem/difficult phase lasts for more than half a year - the problem solves itself, and things are back to normal.

If you suspect, though, that he is avoiding playing with you for other reasons, it would be best if you asked him directly. I wish you good luck, anyway.