Highest and best offer on a REO?

I was looking at a property and was not in the position to make an offer. It was a highest and best offer deadline of 1/6/2016 so I could not make an offer. Then listing said Back on the market! I made an offer 1/19/2016 and they came back today 1/22/2016 with highest and best with new deadline of 1/25/2016. I sent my highest and best offer do they have to take the highest and best or can the keep putting it back up on the market. Also how long do they have to get back to me on my offer? Thanks
Added (1). Ok thanks I guess on 1/6/2016 all the bids where too low and all rejected.
So this round I might be in the running I went 15% below the asking price.
Added (2). It is a bank owned home that is foreclosed. I am using a real estate agent They listed it 10/15/2015 and lowered the price two times. This house is a total rehab for an investor it would be a tear down. I would live here and redo everything. My house sold an closes at the end of the month. I can buy this property cash and rehab it. I do not need a mortgage anymore and be willing to ruff it for a few months.

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