Technically, there never was a "deathblow", since the LeSage Theory is still alive and kicking - but with a very small audience. This should not be too surprising, since there are still strong proponents of the luminiferous ether.
However, the most obvious, and strongest problem, is the viscous drag which such a mechanism produces. If the flux has an effective rest condition, in which the net force on an object is zero, then any relative velocity will produce more collisions on the "leading edge" of the body than on the "trailing edge". This is because the slower particles which would normally impact on the trailing edge will not catch up, so no impact. Likewise, the impacts on the leading edge will be stronger, due to the increased velocity of impact. The result is that any moving object will be slowed down and eventually come to rest. The consequences of this to any planetary system should be obvious.
Richard Feynman talks about this in one of his lectures, and this forms the first 4 minutes of this video However, note that the rest of the video discusses why the maker thinks Feynman is wrong - the theory is not dead.
Another video addresses other issues and how physicists considered working around them.
The "obvious" concept of the LeSage theory states that each mass reduces the number of flux particles by absorbing them. Maxwell pointed out that the energy released by this absorption would heat the body, and we don't see any such heating. As a matter of fact, all matter in the universe should be quickly vaporized.
You can get around this by assuming that the particles are tiny and very fast - but other constraints require that the particles travel much faster than light, and this is not a popular position post-Einstein.
You can get around this by assuming that the collisions are only partly inelastic, but then ...
And you get around this by ...
Well, you see how this goes. The situation is very similar to the ether theory, in which the Michelson-Morley experiment is explained by the concept of ether drag, in which something very much like viscous drag causes the ether at the surface of a planet (hint: the Earth) to become stationary at the surface so no velocity of the ether is observed. That this causes other issues can be dealt with by the application of great ingenuity, and the struggle goes on for those who favor the ether.
It should be noted that, as the technology has improved, the Michelson-Morley experiment, or its equivalent, has been repeatedly performed, each time providing a lower and lower limit on the value of the ether wind at the Earth's surface. The current value is phenomenally small - on the order of 3 nanometers/second. But it's not zero.