The article mentions that gravitational interaction with the two moons of Mars, Phobos in particular, would be a factor that would require station keeping.
This 2012 paper discusses locations in the gravity field of mars where a Areostationary orbit would be possible due to small variations in the gravity field of the planet. Certain points seem to be slightly stable, and satellites put in certain particular locations above the Martian equator would tend to stay there, although they would be orbiting these locations by a few degrees. If the wobble it too large, it sort-of defeats the "stationary" part. You'd have to do some steering, and at that point it would be better to just call it a synchronous orbit. (Fixed dishes will be superseded by steerable phased arrays well before then).
However, once I started seeing terms like monodromy matrix and heteroclinic orbits in that paper, I decided to ask here instead.
Question: What factors would make station-keeping of an Areostationary Mars satellite necessary? Would the pull of the Moons destabilize orbits at Mars' natural gravitational Areostationary points over the period of years, requiring station-keeping?