Every lender has different rules they follow but there are guidelines we can use. I will base this on a price from 2005 or 2006 as a starting point.
If the market has dropped 20% from 2005 that would give you an approximate fair price for the market. This is driven by location and condition. The lender would order an Broker Price Opinion (BPO) to verify that number and typically would accept something in the range of 20% less than the current market (BPO) value. This is where the lender rules come in. Some can only accept an offer of 88% for a VA loan or 82% for an FHA loan. If it is a conventional loan then the rules are different and it could be less than that.
If you are offering less than 80% then they will likely reject it or hopefully counter offer something they will accept. If they are rejecting the offer without a counter then the price was just too low for them to accept and start negotiations. Everyone expects to end up in the middle between the asking price and the offering price. It doesn't always work that way but many times that is how we start out.
I have done several short sales successfully and it can be done. You have to realize there are lots of buyers out there looking for a deal and some are trying to steal but if you are willing to work on it you can get a good deal today. If I can help you please just email me back.
Hope this helps.