I would suspect he's already in a relationship

Red flag for sure.

No, he's asking u not to...

Married or otherwise committed.
That would be my initial take.

gemi30 are you prepared to accept this if he does not talk about it how an earth can you get to the bottom of it and help him whatever it is that could break you up i am sure it need not come to that and you can work it out

When you say "specific times" - are you saying this is outside normal working hours?

It sounds as though he's afraid of what you might think of him, and that you'll decide to leave him if you don't like what he says.

Is he getting chemo or dialysis or something like that?

He sounds like a married man to me...

Doesn’t sound he is keepworthy!

Sounds like he's in a relationship, have to agree with the others here.

He’s dying

Drop it lol