The support of solar prominences is normally described in terms of a magnetic force on the prominence plasma that balances the solar gravitational force. Because the prominence plasma is only partially ionized, this support needs to be understood in terms of the frictional coupling between the neutral and ionized components of the prominence plasma, the efficacy of which depends directly on the ion density. More specifically, the frictional force is proportional to the relative flow of neutral and ion species, and for a plasma with a sufficiently small vertical ion column density, this flow must be relatively large to produce a frictional force that balances gravity. A large relative flow, of course, implies significant draining of neutral particles from the prominence. We evaluate the importance of this draining effect for a hydrogen-helium plasma and consider the variation of the draining with a variety of prominence parameters. Our calculations show that the loss timescale for hydrogen is much longer than that for helium, which for typical prominence parameters is about one day.