Unfortunately, if the bank won't accept your offer,the next indicated step for the agent listing the property would be to look at any back up offers that came in(that perhaps were not submitted until the bank rejected your offer),that came in. Although I don't know what your agreement said verbatim, once the bank says no, and you decide you do not want to come up to the price they are asking, the only other alternative would be to submit other offers. Hopefully the agent who submitted your offer stuck to their original agreement, and it wasn't until the bank countered that they submitted other offers. I don't know if they can legally accept that kind of agreement in the first place....a grey area perhaps....
I do agree with Tim Moore and Rachel Neal's answer below, although there are rare circumstances where you can try to get an agent willing to go the extra mile, by helping you get in a position to make a strong offer and come in quickly. My partner called the bank that foreclosed on a property before the property was listed with a local agent. She found the agent it was listed with and had discussed a fair market value for the property that the bank would be willing to consider and had it ready before any other offers came in. Also, an estimated price on Zillow, or any other site, is not as accurate as an agent who knows the current market value of property and is in the business of selling homes.
Sorry to hear that you are having a difficult time finding an agent to work with that will help you find a property in you price range. It may be that the agents are steering you into a better investment. For example: I have worked with clients who ask for mobile homes in the 50k price range, who were under the impression that they paid for it and they didn't have to pay extra.Then I have had to inform them of the monthly space rental fee of about 600 dollars. In this case, it may be wiser for them to place 50,000 down on a property, and pay a small mortgage....depending on whether they qualify for a loan. Cash does work, but it is very difficult to find inhabitable private property for 50,000 or less.
Check this out: http://www.zillow.com/wikipages/what-is-a-zestimate/