They get trained before release. On general information. But they don't improve while working on very specific tasks. Every new session is like an experienced human on their first day at a new job.
Unique skills and jobs do exist. And LLMs can't gain additional knowledge "on the job" like humans can. They are generalists, that can only be steered by prompts, skills and context. Thats all I'm saying.
This fact is currently the most limiting factor for LLMs.