NASA is putting pause on sending commands to its Mars exploration instruments from November 11 through November 25 as it waits out the Mars solar conjunction. With the sun in the way, any commands sent to Mars could suffer interference capable of harming the robotic explorers.
They are much more stable than other locations but are not completely stable, so station keeping is required. In a theoretical two body system Lagrange points would be perfectly stable but that is not the case with the solar system. Eg: The orbit of the moon ever so slightly effects the Sun - Earth Lagrange points.
The JWST is a good example. The expected observational lifespan of the telescope is based on how long it is able to remain at L2.
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I thought L1, L2, and L3 were unstable but L4 and L5 were stable. Hence why asteroids and other detritus tend to collect at L4/L5.
Edit: Huh, it looks like the stability of L4 and L5 are dependent on the mass ratio of the two bodies. The ratio works out for the Sun-Earth system, so it should also work for the Sun-Mars system.