re: Mechanics. Diagnose this (video)

Sounds like brake booster. If your under 150,000 miles take it to the dealer and reference:

13N02 – Extended Warranty Coverage on Brake Booster – 2010-2013 Ford Edge & Lincoln MKX

PROGRAM TERMS
This program extends the coverage of the brake booster to ten years of service or 150,000 miles from the warranty start date of the vehicle, whichever occurs first. This is a one-time repair program. If a vehicle has already exceeded the mileage limit, this coverage will last through January 31, 2015. Coverage is automatically transferred to subsequent owners.

VEHICLES COVERED BY THIS PROGRAM
Certain 2010-2013 model year Edge and MKX vehicles built at the Oakville Assembly Plant from May 3, 2010 through March 28, 2013. Affected vehicles are identified in OASIS.

REASON FOR PROVIDING ADDITIONAL COVERAGE
In some of the affected vehicles, it is possible for the brake booster to develop a small tear in the diaphragm under certain driving and environmental conditions. If this occurs, the driver may hear a hissing noise while depressing the pedal and may also experience a “spongy” pedal feel without a noticeable effect on braking performance. If the vehicle is not serviced, the tear will eventually expand and the pedal effort required to stop the vehicle will gradually increase. However, in all cases, the fundamental vehicle braking system remains functional.

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