Author has written 8 stories for Protector of the Small Quartet, and Beka Cooper series.
It's spelt INCORRIGIBLE, not 'encourageable'.
Incorrigible, derived from the french 'corriger', means: (of a person or their tendencies) not able to be corrected, improved, or reformed.
Encourageable is not actually a word. For a refresher, though, 'to encourage' means: to give support, confidence, or hope.
I'll leave you with some examples:
She was an incorrigible flirt.
He was an incorrigible drunk.
"Meathead, you are INCORRIGIBLE!"