Banks often don't act "rationally" until you understand how they work. We listed a short sale for 160k, got an offer for 150k., bank didn't take offer, foreclosed and re-listed for $140k. Go figure.
But, once you understand the process, it all makes more sense. You see, banks typically aren't really the "lender". There is some outside investor that owns the loan (often times, Fannie Mae or Freddie Mac) and the "bank" you are dealing with is actually the SERVICER of the loan.
So they have a servicing contract.... I don't know how much they get/month per file.... it might be more like a lump sum for 2 million files. They are paid to collect payment, deal with loss mitigation and REO's. When they are collecting payment, they are making money (although a small amount per file). When they are working through loss mitigation or REO's, they are NOT making money, they are spending it.
Therefore, loss mitigation departments and REO departments are set-up to be the least expensive they can get away with under their servicing agreement... which is why short sales now take an average... yes average... of 7 months!
As part of their servicing agreement with the investor, they have underwriting guidelines. The underwriting guidelines tell them who to loan money to, but also how to conduct a short sale, or an REO sale.
They will follow those underwriting guidelines to a T because they are contractually obligated to. Besides, they don't care what your property sells for... they just want to fulfill their obligation under their servicing agreement, meet the underwriting guidelines and do so as cheaply as possible (minimum wage or automated systems help with that).
So I'm sure the underwriting guidelines for the house you are bidding on, stipulate a listing price equal to or close to the BPO (Broker Price Opinion), with subsequent regular drops, and that allow the lender to accept an offer that is within a certain percentage of whatever the current list price is.
You can't convince them to take something different. They have no incentive to.. that would jeopardize their servicing agreement.
So, they ARE acting rationally.... even though they aren't :)