From the perspective of electromagnetism alone, so long as the holes in the mesh are much smaller than the wavelength of the electromagnetic radiation to be reflected, there isn't much of a difference between a mesh antenna and a solid antenna. The radiation cannot get through the small holes. This is, for example, why one should stay in ones car during a lightning storm. The car's big windows are invisible holes at the very low frequencies of a bolt of lightning.
An example closer to the problem at hand: A mesh with 1.4 mm holes (e.g., a square mesh made of wires separated by 1 mm) will appear to be quite solid to electromagnetic radiation with a wavelength of 1.67 cm or longer. That includes the Ku band (wavelength between 1.67 and 2.5 cm), and everything with a wavelength longer than that. (A mesh antenna intended for the Ka band would require an even finer mesh.)
However, these electromagnetic concerns are not the only concerns. A fine mesh made of flimsy wires might fall apart when transported back and forth across the country, not to mention falling apart during the rather rough 8 to 10 minutes that follow launch or falling apart due to the sudden jolt that occurs when the upper stage reignites. The significant mass savings that can result from using a mesh antenna versus a solid antenna amount to nothing if the mesh antenna fails due to its inherent flimsiness.