The next day I received an email informing me my offer had not been accepted, they advised the minimum they would accept, and I was told I could submit a counter-offer...by midnight that same day. 

The asking price was $35k from the bank but the investor held his ground for 3 weeks and only went up to $9k and got the property from the bank who kept saying they would not go lower with every counter offer they made.

Or should I just make my best offer from the start, knowing that if they come back with a higher counter offer the numbers probably just wouldn't work for me and I'd have to walk away?

If you have any counter offers suggestion or just think this deal is worthless, please. tell.

I put the offer in on Thursday, they did a counter off and I accepted their counter.

I am getting more counter-offers on my low-ball offers, so the excellent litmus test tells me that sellers are becoming more willing to negotiate as the buying pressure slows.  

Except there might very well be five or ten rounds of offer and counteroffer...

The inspector finds a lot of problems ( many were obvious pre offer) seller comes back with a lowball counter offer knowing he was going to do that in the first place.

I'm a little miffed by how rude he was, not even counter-offering, it's not like I was low-balling.

I made an offer on a foreclosure (REO) property in my area.  The company handling the foreclosure for the bank accepted my offer 3 months ago and informed us that the bank would take about 4 months to close the deal. ...