Does China have an equivalent to NASA's Deep Space Network tracking stations? By deploying large antennae in the US, Spain, and Australia, the US was able to maintain 24/7 contact with the space missions. Granted, this isn't a manned mission but I'd still think that they'd want to have continuous comms to their lander.
There is little value in the continuous comms to the unmanned missions. You generally want good tracking during maneuvers (which is where things go wrong), but outside of those motion is highly predictable. And the comms to the unmanned missions are mostly for forensics (outside of active science or other active payload functions) -- if a problem arises that the automation on board cannot solve it is highly unlikely…
It's one thing to have to wait 16 minutes to grab telemetry and issue commands to something on Mars, but having only a few seconds lag seems like something mission designers/operators would take full advantage of. The idea of actively controlling a rover rather than having it perform pre-programmed routines seems highly desirable.