Hun, my mum & dad just sold their house & they had one person hang on for months negotiating.
Eventually he refused to budge & so they dropped their price. It was around 20000 less than they wanted, but in the end they also wanted a sale.
I think stay where you are. Maybe tell them to take it or leave it. I've never heard of a RE doing that & I really don't think it'd be for your benefit if you agreed.
It sounds like they have noone else interested. Goodluck