I am another with this problem. I brought my 2007 Edge, 15600 miles, AWD to Midas for an oil change and the mechanic there told me about a "transmission leak" that he had found, but couldn't trace where it came from. He told me that the transmission fluid level was fine though.
I dropped it off this morning to the Ford dealer (Ford of Hyannis) and was told that the leak is caused by a bad axle seal. The part is on order and hopefully will be in tomorrow.
After reading the many posts on this problem, I do recall smelling the burning smell after stopping. It only happened a couple of times and I wasn't sure if it was coming from my vehicle or not. I guess it was.
Thanks to all who have posted here about the leak problem in the Edge. Hopefully, the replacement seal will work and I'll be all set. We love the car otherwise.