It is not unusual for a bank to accept an offer they previously declined, if they do not receive better offers. My customer just closed on a foreclosure whose asset manager had originally declined our offer and countered at full price. For about 2 weeks, I periodically asked the listing agent to resubmit our offer. The bank gradually lowered their counter offers while we held to our original offer. Our offer was based on a comprehensive CMA, hence, we were negotiating from strength. I do not know the particulars of your situation but if your price is realistic, based on comparables, keep resubmitting your offer while you still look for other properties. You have nothing to lose.
You never know what lenders will do have your agent work it and see where it goes.
Carmen is correct. Re-submit your offer. Estate Properties (my brokerage) just closed several bank REO (repo/foreclosure) in North Idaho - one with a similiar situation to yours.
Although many bank REO's in North Idaho are selling close to asking price, we made the case for these clients (with assistance from their bank) that the offer they were making was the best they could do (as it truly was the case). Therefore, with the assistance of a realistic, professional listing agent working with the bank, the Buyer's were able to successfully get the property for the price they offered.
The key here was to prove to the bank that this is the most you can spend, or you simply can't buy it. If this is an honest request, they could review it, and accept it....
On the other hand, if you simply want to pay less than the bank is asking, and they have no other offers, you can, as Carmen suggested continue to submit your offer, and hopefully prevail based on tenascity alone!
In either case, don't give up....work closely with your Realtor, and you'll be one of the many fortunate buyer's to take advantage of the great buys on bank repo's here in North Idaho!