If they say it is final accept it as not going to happen. Then tell your realtor to tell the other realtor they just lost a sale. Walk away and who knows, maybe the seller will change their mind. After all, a buyer in the hand is worth 100 on the road going to look at other places.
Homebuying and negotiation is like a dance, give and take. A successful transaction depends on a lot of factors and a big one is the seller's motivation. If the seller is in financial trouble they may not be able to take less, i.e. upsidedown in their house, or their house is worth less than they can receive in the market.
My advice to you would be to get as much data as possible to accompany your offer and go as low as you think the data supports. A recent appraisal or a CMA and being represented by a good Realtor will help you establish a value and help you get a deal!