Holy shit, I feel the same. I was arguing with an LLM one day about how to do Kerberos auth on incoming HTTP requests. It kept giving me bogus advice that I could disprove with a tiny snip of code. I would explain. It would react just like yours. After a few rounds, it would give the first answer again. Awful. So infuriating.
I had a similar issue with GNU plot. The LLM-suggested scripts frequently had syntax errors. I say: LLMs are awesome when they work, else they are a time suck / net negative.