We consider the factors which limit electron wave coherence in open quantum dots, through a study of the reproducible fluctuations in their low temperature magneto-resistance. Our investigations indicate that at temperatures well below a degree Kelvin, electrons are able to propagate ballistically while maintaining phase coherence over very long time scales. Indeed, simple calculation reveals that electrons may undergo as many as a hundred collisions with the confining walls before coherence of their wavefunction is fully randomized.