Capability
Dependability, Resourcefulness
noun
Remember how 甲斐 can mean "worth"? If worth is in your nature, you're probably a person of some capability. You're worth knowing and people appreciate your dependability.
甲斐性 means being dependable, responsible, or resourceful, especially in supporting others financially or emotionally. Traditionally it refers to a man's ability to provide for his family, so 甲斐性がない is often used to criticize someone for not making enough money.
This word combines the word 甲斐 (which you've already learned) with the secondary on'yomi reading for 性. You haven't learned this reading of 性 yet, so here's a mnemonic to help:
Who embodies capability and dependability? The Shogun (しょう), of course! He feeds his entire clan and army, makes battle plans, and rules a nation — all without breaking a sweat. A true leader, dependable and strong, the Shogun gets a lot of love for his 甲斐性.
どうしてあの甲斐性無しが彼女の愛を復活させることができたのか、全く理解できないね。
I really can’t understand how such an incompetent man like that was able to rekindle her love.