Is there a word or phrase that means someone who doesn't learn from his mistakes or makes the same mistakes again? It can be a noun or adjective or anything that implies the meaning.
In the criminal justice world, they are known as repeat offenders. There is no reason that phrase could not be utilized (a bit poetically) to other spheres.
A similar term is recidivist
Denoting a person who repeatedly reoffends
A common quote, often misattributed to Einstein, is
Insanity is repeating the same mistakes and expecting different results.
It likely was first used in publications by Narcotics Anonymous.