If your agent did their job correctly, they based their advice of a price to offer on a market analysis, tax records, current market condition and condition of the home your are interested in. Based on this information your offer should have been within the 10% range of the market analysis, so if the bank/lender rejected your offer, that offer is officially closed/dead. However, you can submit a new offer with better terms and/or more money, but be realisticabout offering more. There are a lot of good home on the market at affordable prices, don't be house poor. Remember, don't be afraid to keep looking. There is a home for every person, you just have to be patient, persistent and educate yourself as to the home buying process.