The air flow sensor and throttle position sensor are only covered by the
basic 5/60 bumper to bumper warranty. Throttle position sensors tend to
work sometimes and not others. Simply unplugging it and plugging it back
in during their testing may have been enough to make the car run better
for a while, but I'd bank that you'd need the throttle position sensor in
relatively short order. The transmission computer uses the value from the
throttle position sensor to help it determine how and when to shift the
transmission, so a bad reading would likely cause the symptoms you
describe.

The air flow sensor is unlikely to cause any transmission issues, but may
make the vehicle have poor performance as well as turn on the check engine
lamp. It sounds like the dealer is most likely correct on at least the
throttle position sensor.