You need to find out what the banana delivery schedule is, hijack the truck and take the monkeys back to jungle.
If a listing has an offer, then the buyer backs out, they have an in-house system that can state "if this happens, then go back on the market at a certain price so much less than the old price.
I was representing a buyer on an REO, we offered OVER asking price,our offer was not accepted, the winning offer backed out, and they want BOM with a price lower than the what we offered....so we offered MORE than the first offer...and we got it. We determined that the lender was working from formulas that did not in fact represent market value.
It appraised for more than our purchase price.
Your question takes for granted that the bank (like sellers) has emotions and/or a bottom line. The reality is that nobody knows what the formula is that the bank uses (except the bank) and why they choose to accept some offers and reject others. Ultimately they are working with algorithims, balance sheets, and other complicated financial instruments to determine whether or not an offer is acceptable at that given time. While it makes the most sense to us that they sell it at the highest possible price in the shortest amount of time - often this doesn't play into their formulas.
You also assume that the bank has the benefit of foresight and knows what the property will sell for in the future. Right or wrong they may assume that they can sell it for more if they control the entire transaction, but the reality is that don't know what it will sell for - no more than you or I do.