How do you handle customers who refuse to split the difference?

Hi everyone,
I’m fairly new to car sales and I’m trying to improve my negotiation skills.
One situation I struggle with is when we’ve gone back and forth, and my manager asks me to try to split the difference with the customer. Sometimes the customer immediately says something like, “No, I’m not splitting the difference,” or “You need to come down to my number.”
In those moments I kind of freeze because I’m not sure what to say next without sounding pushy or repeating myself.
How do you usually respond in that situation? What questions do you ask to keep the conversation moving? I’m looking for advice from experienced salespeople on how to handle this professionally.