If it was MLAT and you were not one of the receivers providing the data Flightaware uses to calculate position then eventually, after a matter of minutes, Flightaware will cease feeding MLAT information back to you about that plane.
You could try searching Flightaware.com for the flight and see if there is any other information. If you find it you can look at the tracklog and see what info you provided as well as more information to see if it was on the deck and going slowly enough for that aircraft to have turned off to taxi.
@wiedehopf, @SweetPea11 - I checked the flight log and it was MLAT all the way. From looking at the flight data, it did indeed land and was on the ground for a while then flew back to its home airport.
MLAT was the correct answer all along and now I know what to look for to know. Thanks!