They can ask once. After that, I'll set my phone in my pocket to record before going in to a private meeting.
In many states, you will have committed a felony by doing so. It is, in many jurisdictions, illegal to record a conversation without informing the other party. If you think that, because the other party is asking you to do something illegal, that you are off the hook, you are incorrect.
I knew someone who did as you suggest you will do. The supervisor that was asking the person doing the recording to do something wrong got a reprimand but is still employed. The person doing the recording lost their job and pension in return for their mutual employer asking the DA not to press charges.