Parents often fear that enlisting a family member to help with finances means starting down a slippery slope to losing autonomy. Reassure your dad that it doesn't have to be
that way. Tell him, "I want you to remain independent for as long as possible. My goal is to help you stay where you are and be in control but to have some support. I want to be that support or make sure that you have some. It's just the same as how I rely on my spouse or partner to assist me with financial decisions."
It's important to recognize that admitting to needing help will be hard for your father. Stress his dignity and independence. Even though your dad has a diagnosis of dementia, focus on what he still has rather than what he's lost. Emphasize that given his diagnosis, you both need to plan for the future and prepare for when he does need practical help.
If your dad understands the concept of a power of attorney, assigning one is a good idea. Next, draw up a list of his assets, including account numbers. Reassure him: "I'm not going to be touching your assets, but if something happened to you and I needed to, I would need to know where they are." It may also be a good idea to have your father put your name on a checking account so that if he has to go to the hospital, bills will still get paid. These are all useful steps to take even if your other parent is still well.
If you can't make a good case with your dad, it may be because some parents just have a hard time listening to their children about these matters. Enlisting a third party can be helpful. Sitting down with an impartial professional such as a financial planner, an attorney, or a geriatric care manager may reduce a parent's resistance to addressing matters of money.