In the book "The Martian", communication is lost with Earth after the Mars Ascent Vehicle leaves. It seems to me the Mars Descent Vehicle (MDV), which they landed in, would have had some kind of a communication system. I don't recall hearing anything about the MDV. Why couldn't the communications be used from the MDV, or why wasn't there any communications included?
To quote from the first chapter:
The MDV is basically a big can with some light thrusters and parachutes attached. Its sole purpose is to get six humans from Mars orbit to the surface without killing any of them.
The concept behind the MDV was just to get the crew to the surface. Once there, they would be able to use the MAV to perform communications with the Hermes. It's not outright stated in the book, but I suspect that it was trimmed down as far as possible to save weight and space since there was already a functional MAV on the surface (and the book notes that, if the MAV were not fully functional, they would have just gone home without landing) and probably because communication would be difficult on the descent due to interference of atmosphere, etc. The descent vehicle wasn't going to have to dock with an orbiting spaceship, and no one on Earth would be able to help them if something went wrong, so they eschewed communications.
Additionally, even if it had carried communications gear, it might not have survived. A relevant excerpt from the book:
The MDV is on its side and there’s a breach in the hull. Looks like the storm ripped the cowling off the reserve chute (which we didn’t have to use on landing). Once the chute was exposed, it dragged the MDV all over the place, smashing it against every rock in the area.
It's worth noting that, if you watched the movie, you'd be even more lost because they barely mentioned the MDV at all.
It seems to me the descent stage would have had some kind of a communication system.
While the astronauts are on the surface, they communicate using the MAV. Why put a second, redundant comm system in the MDV which remains on the surface after they leave?
Shipping material to Mars is astronomically expensive (so to speak). The cost is estimated at US$45,000 per kilogram.
The second comm system would be useful only if one or more astronauts were inadvertently left behind. Presumably, NASA deemed this to be too unlikely to justify the extra costs involved.
I think its probable that the MDV did have a communications system, but there is something that is being overlooked here - the MDV communications system does not have to be a high power one, as the only time it was on Mars and manned was when the Hermes was in orbit, meaning that it could use the Hermes communications system to talk to Earth and thus only needed a low power communications system, which saves weight and power.
Once it was down and safe, the crew could use the MAV communications system, which was required to be high power as it needed to be monitored from Earth prior to the mission start.
In short, there is no requirement for the MDV to act in an isolated capacity, so it uses the support systems that are built for it to use.