I was diagnosed with an incurable cancer and I've been given three months to live.
My son is fighting an irreversible brain disorder.
When Koichi fell incurably ill and died, his last words to Viet were, "We will meet again." True to his words, he came back to the office the next day and did everything the same as he had before.
When you can not cure something, this is a problem of incurability.
This is a jukugo word, which usually means on'yomi readings from the kanji. If you know the readings of your kanji you'll know how to read this as well.