Your mother's reaction isn't unique; most doctors have known patients who refused to face their situation. And often there was very little they could do to get them to change.
But there is one thing you can do -- and that is pray. Perhaps you can't make your mother face reality -- but God can, and I urge you to pray that He will. Pray too that you'll have wisdom in dealing with her. The time may well come when she'll need you as she grows weaker, and you don't want to do anything that might cut you off from her. Remember the Bible's promise: "The prayer of a righteous man is powerful and effective" (James 5:16).
Another reason to pray for her is because her problem isn't just emotional or mental; it's also spiritual. God wants us to act responsibly and wisely when hard times come -- and when we refuse, it is sin. Pray that God will convict her of this. Pray too that He will open the door for you to ask her why she refuses to acknowledge what's happening to her. But do so with compassion and gentleness, not rashly or in anger.
Pray especially that she will realize her need of Christ. Some day soon, she must stand before God -- but is she ready? She can be, by turning to Jesus Christ in repentance and faith, and trusting Him alone for her salvation. And if you have never confessed your own need for Christ's forgiveness, commit your life to Him today.