Using his feet in wheelchair.

While I don't know the cause, certainly muscle stiffness, muscle tiredness, or mental tiredness are all completely understandable.

I agree the wheelchair foot plates should be on for any wheelchair travel, to avoid any foot/ankle injuries.

(Exception would be if travelling only a meter or so you could wheel backwards).

Yup, just put the foot rests on so you can easily push him. I imagine it's got to be pretty hard to keep your feet up like that for any length of time.

The very first thing that I would check for is to see if the wheelchair fits your husband properly.

Can you adjust the footrest to be more comfortable for him to use?

Who knows.
What I do know is that I see this a lot, people not using the foot rest when someone is pushing the chair. This is an accident waiting to happen.
If you know you are going to be pushing him put the foot rest on and have him use them.
I can imagine after a long day he is tired and not being able to keep his feet elevated takes energy, concentration and muscle.
If the next day he can elevate his feet I would conclude that he was tired the night before.