The imp is incorrigible: his bottom is still red from his last spanking when he plans the next prank.
The laws of nature and mathematics are incorrigible.
The construction flaw is incorrigible; any attempt to amend it would cause a complete collapse.
His black soul was too incorrigible to repent, even at his execution.
The incorrigibles in the prison population are either lifers or habitual reoffenders.