You were not buying an "REO", you sound like you were in a short sale situation. Let me define the terms for you.
Short sale: Owner is behind on their payments. They are selling the home for less then they owe on their mortgage due to a declining market.
REO: Bank has foreclosed on owner who was not making the payments. Bank now owns the property outright and will usually hire a realtor to market and sell the property.
The truth is, you were never really "in escrow" so to speak. The seller can accept your offer, but it's the bank that really decides what amount the property will sell for. Buyers who attempt to purchase short sales are not in a very good position.
Question, did your agent discuss the differences between REOs and short sales? Perhaps they are not experienced enough to know the difference? You should have waited to have the appraisal done until the bank accepted your offer. Sometimes on a short sale, the owner will have two loans, a first and a second. These type of short sales are hard to close because the second will come back at the end and demand some money. If you won't bump up your offer, they will refuse to sign off on the sale and you are out of luck.
If you are interested in learning about the differences and how to go about buying REOs, contact me and I'll give you some information about workshops where you can ask questions.