Originally Posted by Tim Thompson

Certainly a magnetic field reversal and some loss of atmosphere can be related, but one should not exaggerate the effect. Venus has no intrinsic magnetic field at all, as has already been pointed out. Yet its massive atmosphere shows no sign of going away any time soon. The solar wind interaction with the upper atmosphere of Venus does strip away some of the atmosphere, but only the very high velocity tail of the thermal distribution. Even billions of years of such an interaction could not strip away the whole atmosphere. The main reason for that is that Venus is a fairly substantial planet, with 81.5% of Earth's mass, and plenty of gravity. And since the atmosphre of Venus is 96.5% heavy CO₂, it doesn't go anywhere.

Mars also has an atmosphere mostly made of CO₂ (95.3%), and like Venus, it has no intrinsic magnetic field. But its mass is only 11% of Earth's, and that's a big enough difference to count. It's a good bet that Mars lost much of the atmosphere it might once have had, primarily because its low mass could not hang onto it. So Mars would have lost much of its atmosphere, even if it did have a magnetic field. But being without one allows the solar wind to directly impact the upper atmosphere, increasing the rate of loss.

Earth has more mass than Venus & Mars combined, so it is most capable of gravitationally holding an atmosphere. Earth also has a substantial intrinsic magnetic field, which fends off the solar wind, preventing it from directly impacting the atmosphere, except at the poles where the aurorae are generated by solar wind interactions in the very high atmosphere.

If Earth were to lose its magnetic field altogether, it would still be rather more retentive of its atmosphere than Venus, since the solar wind is weaker at Earth than at Venus, and Earth is so much more massive. But a magnetic field reversal is a transitory event. The reversal will see energy transfer from the main dipole to higher multipoles, presenting an apparently weaker magnetic field, and enabling the solar wind to more directly impact the upper atmosphere. The result will not be any substantial loss of atmosphere, but will be an enhanced background radiation field at the surface of Earth, due to increased solar wind particle impacts on terrestrial atmosphere particles. But I don't think we can predict how much more radiation there will be at the surface, and its biological effect, without a detailed model of the reversal process, which we don't yet have (Glatzmaier's simulations only show in general how the process works, but should not be considered detailed predictions of how it will happen on Earth).