L.M.
Is this just an estimate or has the house been appraised? Also, most companies will not finance 100% of the property's value, so is the $13,000 what you need to bring down the mortgage principal to 100% value, or is it what you need to refinance?
If the mortgage company did an appraisal, was it a true full apprasial, or what they refer to as a "drive by"? My point is you may want to consider having an appraisal done.
You're other option is to talk to a different bank or mortgage broker, but at $13,000 you probably won't have much luck. Just keeping putting extra down on that principal each month and try again in 6 months.