Based on my knowledge, a bank respresentative can accept up to 10% off the appraised value without any managerial authorization. So my suggestion would be to offer just a bit less than 10% off and you probably won't need to wait months for answer.

In most cases banks look to get 80% of what the person owed who was foreclosed. However depending on market conditions they will list at market price than lower the price accordingly the longer it stays on the market. Sometomes there is no rhyme nor reason depending on the bank.