You've established that their comms are FTL (faster than light) boosted by relay satellites. This is a good procedure, but it begs (in my mind) why this can't be applied to objects as well as radio waves. Or, soes Aurora use a modified version of FTL drive to get from here to there without taking a lifetime?
Down on the planet, I'm surprised that the explorers don't carry personal comms units. Even if they are line-of-sight, they would still be functional over a wide range of terrain. These units would have loads of other uses: timing lengths people are gone from camp, intervals between events, etc. Personal units would even be handy in camp from tent to tent.
One single person should not be the holder of important codes such as contacting the mother ship. Too many things can (and did) happen. If each person is given a different code, then Reese, sitting in Aurora, could identify immediately who is calling.
Another problem with ground to Aurora comms: if the planet is turned away from Aurora, how can they establish a circuit? Did Aurora set out a satellite ring in orbit before departing? I don't remember.
Bill