This may sound like a dumb question. Are we sure that the dealer that is doing the service is using the correct air filter. Briggs has two air filters that are almost identical to each other, but slightly different height, and different filtering media. If you install the wrong air filter it will do what your mower is doing within a few hours of replacing the air filter.
make sure you have the 692519 air filter and not the 694018. The other thing to check is make sure it has the RC14YC or equivalent spark plugs, and not the RC12YC, because they will cause the same thing. Rich running. no power.