That's a tricky issue.
It sounds to me like you're on time with your mortgage payments yet you're approved for short sale, this is good for you. I have closed a few short sales where the owner is current on payments.
I would really need you to email me directly to give you the best possible answer.
I don't see why the buyer needs a THIRD extension? BUT it will likely be better for you, to let the current buyer close, if they can. It will take longer to get a new buyer approved, maybe 60+ days. Then again, I don't know how long it's been since your current buyer has been extending their close of escrow & how much longer they want the "4th" extension to close, to be. ?
I have a LOT of experience in this area, I'm happy to help. Please shoot me an email directly, I don't look back on this same Trulia posting for answers after mine.
Emily S. Knell
Realtor Since 1996
Realty ONE Group
Short Sale Listing Agent w/ 97% success rate
100% Success Rate in CA
Closing short sales within 300mi of my home!