To be fair - and I mean this in the most supportive way possible, just thinking that a different perspective might be helpful... it seems to me that you are both playing games. I don't mean that in a bad way but this is how people do business. You were happy with $4000 less but tried to get more. Well aware of the housing market, they very well might have said to themselves after your counter offer, "I don't like the sound of them either. I think they are playing mind games." If they felt that their offer was fair and felt you were being greedy, they might have gotten aggravated and decided that if you didn't want to play nice (not saying you weren't - just that they might think so) then they aren't.

Good luck.