Michelle, banks operate on their own schedule and to achieve their own goals. Those may not line up with what you want. A short sale actually refers to the fact that the selling price is expected to be short of the mortgage amount. The banks are anything but quick about agreeing to take a shortage.
If the loss mitigation department accepts your offer, then they have to notify the foreclosure department to stop proceedings. We have actually been caught in a situation where the shortage was zero, so the foreclosure department did NOT stop.
You can attend the foreclosure auction with cashier's check in hand to buy it from the bank's trustee on the first Tuesday each month. The bank will bid the amount owed on the loan. If you bid higher, it's yours, but you have to pay right then and there at the courthouse. Usually, it is better to let the bank take it, and then they will offer it again later through a Realtor. You will have time then to do inspections and get a mortgage loan of your own, which you won't if you buy at the courthouse steps.
The bottom line is that the bank decides (sometimes strangely) and they can supersede a pending contract for sale by foreclosing the property. If your earnest money is being held at a title company, you will get a refund fairly easily.