He is being unreasonable... however he is likely absolutely terrified he'll drop dead any minute.
He needs to learn how to let go of this, get over it and live his life, or he won't have a life worth living.
I would highly recommend you get him to seek some counselling - and do what you can to provide him with sensible safety stuff, ways to contact you, phone always on him so he can ring 999, GTN spray on hand..
But, gently, he does need to figure this out for himself and you may need to point this out to him - fetching his own drink, making his own sandwich, moving around the house slowly, having a sit down where necessary - all perfectly normal, reasonable things to be doing at this point and NOT doing them will not help his recovery.
Living with the abject terror of dropping dead at any second is just not sustainable, either the stress of it finishes you off, or you get the fuck on with life. I chose 'get the fuck on with life' and I am now some 15 years down the road from a 'you won't be here in 5 years time' DX (heart failure, severe damage to various bits of it).
Anyone could drop dead at any minute from an undiagnosed heart problem or aneurysm or seizure. Life is incredibly fragile, does he want to spend the rest of his sitting about waiting for it to happen, or would he like to get on with that life and enjoy it?