It was quickly pointed out that in order for this theory to work, the collisions between these gravitational particles and the rest of matter must be inelastic, that is, the particles must lose energy in this collision. Without this condition the net force on the object would be zero. However this raises another concern, if the particles lose energy, then the object they react with must gain it in order to conserve energy. In this case, over a long enough period, objects would grow hotter and hotter until they melted. A simple calculation shows that in order for the Earth to remain in orbit around the sun, the energy transfer would result in the planet being much hotter than it already is.
Another problem was later brought up, a simpler argument but one that only became "obvious" with the introduction of mechanics based on a frame of reference. When the particles interact with the matter they will be moving in a particular direction. If these particles move at any speed slower than instantaneous, this will lead to an apparent drag. Consider the gravitation of the Sun on the Earth, in the LeSage model the attaction of gravity is due to a slightly smaller number of particles on the "sun side" due to the Sun blocking some of them out. However this picture ignores motion. If you consider the same picture from a frame of reference where the Earth is motionless (consider the view from a camera looking at the Earth from the Sun), then it should be clear that the particles are not only travelling directly "out", but that they are, from the Earth's perspective, travelling to the side as well - opposite to the direction of the orbit. If the particles are to have any effect on matter at all, they must logically then drag the Earth, slowing it down. In order for this effect not to be noticeable on a large scale, they would have to move many orders of magnitude faster than light, contradicting relativity, but proponents of the theory assume the existence of a luminiferous ether which reproduces effects like Lorentz contractions mechanically, much in the manner Lorentz initially thought of them.
A final consideration is that if the gas is truly universal the effects would, over long distances, lead to a net zero force. This disagrees with observations of the large scale structure of the universe, where matter has "clumped" into very large scale structures that would require a long-range gravitational force.
One prediction of this theory is deviations from the inverse square law for sufficiently large matter, because eventually, most of the LeSage particles would be absorbed/scattered by the body and no greater screening could occur.