There are a few potential problems here. It's likely that upon your father's death, the state Medicaid agency will seek reimbursement from the house for what it has paid for your father's care. So you may be paying to preserve the house simply to, in effect, hand it over to Medicaid when he passes away. You may be able to prevent this from occurring by transferring ownership into joint names with yourself, so it passes automatically to you at your father's death. However, Medicaid laws are written to prevent such steps by imposing an ineligibility period of up to five years for any transfer.
This sounds bleak, but there are some exceptions to these rules in certain circumstances. We strongly recommend that you consult with a local elder law attorney to learn how these laws are applied in your state and whether there are steps you might take to protect the house. Yes, lawyers are expensive, but so is paying the mortgage on a house that may simply pass to the state. To find an attorney near you, go here: https://www.elderlawanswers.com/elder-law-attorneys.