Originally Posted by Cubdriver

Au contrare, precession is what they are designed to do. Turn left, precession makes the DG change heading, the turn coordinator and attitude indicator tilt. You are lumping benefical and nonbeneficial effects into one. As EWFflyer said, the actions of dirt and other misgivings cause the gyro to receive impure inputs that are also called precession but are not desirable.

The reason attitude indicators can not be expected to drift is they are spun in the level plane. They constantly correct by the action of gravity, just as a plumb bob corrects itself. If however you feed in some lengthy input you will see that eventually it can't correct fast enough and you will get a tumble. Try it carefully sometime- do a steep turn and just keep flying the turn until the attitude indicator tumbles. It happens sooner in airplanes with clunky old horizons, I can't really say how long it will take in a newer aircraft and it may not happen at all. In older aircraft it only takes maybe 5 turns.

Here's a nice link on this subject.