How to get my grandmother to accept that my dad's condition will never improve?

I think one of the keys here is that your father "consistently refused to participate in therapy." Therapy doesn't work if the patient doesn't do it. I agree that at this point some pathways in the brain are dead. However, as I understand from reading articles on stroke recovery, the brain can develop new and different pathways. Unfortunately if your father doesn't work at it A LOT he will not get better.
If he's on medications there may very well be side effects that interfere with his physical and cognitive abilities. There's a reason those medications are by prescription. They all have side effects. I have had close relatives whom we thought were ready for the nursing home and it turned out to be effects of medication. I have spoken to more than one doctor who said they have seen patients get better when they were put on hospice because they were taken off their meds!
Perhaps you and your grandmother could do some research together. Ultimately his condition may not improve but maybe your relationship with your grandmother will. At least you will have comfort in knowing you did everything you can, which may be what your grandmother is struggling with right now. Best of luck to you.

Might be easier to schedule a visit with his doctor to discuss your father's condition. Many of an older generation will accept the facts from a trusted professional rather than a younger family member.

She's holding onto hope -- that's all she can do. I don't see any reason to try to get her to admit he won't get better, but if you want you can point out that two years post-stroke, improvements are almost non-existent.

Parts of his brain are simply dead and gone, and no amount of therapy is going to return them to functioning.
The therapy he's supposed to be getting is to keep from losing more functionality, but it sounds like that's not happening either. It's just a long, slow decline with an inevitable end.

BadNewsBearer: This, too, was a friend of my late mother's who had asked me such questions after my mother had suffered an ischemic stroke, e.g. "Is your mother getting any better?, How is she today?, etc." This lady, while having good intentions, was unable to grasp the magnitude of such a medical trauma. Perhaps your grandmother is unable to grasp such trauma of her son's. I am sorry that your father suffered a hemorrhagic stroke.

You quite honestly cannot convince other people of anything. If a doctor can't convince your grandmother, then how in the world could you do it. Just keep repeating the facts and with time more acceptance may come. I wish you the best and am so sorry you all are going through this.

I'm so sorry that your Dad's health is failing. Can you talk to his doctor and find out if it's possible to phase out some of his medications or cut them down? Maybe he will do better without so many medications. It may be kinder not to discuss your assessment of your father's health with your grandmother, but rather to explain that he's in a good facility that is providing necessary care and rehab, and that his doctors also are prescribing medications that are needed. Remember that for a parent, one of the worst things that can happen is to lose a child. Your grandmother probably has this anxiety. All the best to you and your family.

Remember she is his parent. We all fight to the end for the lives of our children. Be patient and include her as much as is comfortably possible.

A sad lesson from this is the need to check daily on aging family members, and/or a medical alert device. My mother, 1,000 miles away, had fallen and lay on the floor until found by neighbors on the third day. They usually checked in her daily but had been away for the weekend. I called once or twice a week. Should have been daily. I am now 86 and my own children do not check on me. What goes around comes around. Sad.

How often does your grandmother see him?
What are their respective ages, by the way?

My guess is that you usually have a conversation with your grandmother about this, to explain things. It might be worth trying a different approach, not answering her except to encourage her to go into more detail about her ideas. What sort of ‘better’ facility? What extra care do you think would help? What were the problems with the old therapy? What do you think could be different? Have you done any research into other methods? What drugs do you think should be dropped? Etc etc.

There’s a chance that she’s never got into much detail, doesn’t feel that she’s been taken seriously etc. Listening to it all, giving her follow-up jobs, facilities to visit, things to look up on the net, might really help her. You’ve probably done it all, but she probably hasn’t done it all herself – or she has not taken in all the detail. It will probably be difficult for you to listen without explaining, but it might help her.

If not, there’s always mashed potato! Sometimes I think that ‘magic’ ideas (if they aren’t an rip-off) are useful for people to pin their faith to.

I’m very sorry your family is going through this. My mother had a huge hemorrhagic stroke, initially we were given great hope for recovery. She was transferred to rehab and began intensive therapy. Despite all efforts, both hers and the therapists, no progress came. After some time with no documented progress there was no choice but to discontinue therapy. Insurance doesn’t pay for therapy without progress. My mom lived four miserable years in a pitiful condition, I truly hate to hear of it happening to anyone else. Your grandmother may need to have time to see for herself that things aren’t going to improve, sometimes acceptance comes in stages, and maybe she’s just not there yet. I wish you all peace

I am not a psychiatrist, but ask her tell you how she feels and ask her "what should we do if new treatment doesn't work"? Once you've listened to how she feels, then flip it and say something like "You know I keep thinking that if we just find the right treatment plan he'll get better. But as I talk to more and more specialists, I'm beginning to think that the only way this is going to improve even slightly is if he were to start therapy. But I think that we also need to start preparing for the possibility that he might not get better, as scary as that is."

I'm not sure that this is the correct approach; I'm just trying to brainstorm a way of getting your grandmother to talk about the fears and emotions (and hope) that have her thinking that things can radically change.

Sending good thoughts.

You can’t. She’s in denial. So don’t let her take charge of any of this. He needs the best care you can find for him. Oh, and my aunt said my dad had a good chance of recovering from cancer if we’d feed him mashed potatoes. Old people get foolish ideas sometimes, but that doesn’t mean we should do what they say. Very sorry about your dad.