A New Dark Age
We live in a decaying civilization. It appears to be at the stage of the Roman empire circa A.D. 200 ... still strong but on the way down. It will certainly last out several more generations. What will bring it to an eventual halt is the expansion of the population in concert with the near total absence of any "global intellect", i.e. the Earth has no mind to speak of. We stumble along like an imbecile incapable of organized reason. While there are many good minds, they have no real influence on the course of events which are primarily emotion driven.
I compare a dark age to civilization falling asleep in the manner of an infant who doesn't want to sleep but must. Maybe we need a "nap" but a new dark age is not absolutely certain. It could be avoided in any number of ways. Pick one.
Radio Free Mars
Assuming that a new dark age does develop, it would be advantageous to bring it to an end A.S.A.P. A 100 year dark age is better than a 1000 year dark age.
Thus, an independent colony on Mars is incredibly unlikely to fall asleep at the same time as the Earth. A dark age on Mars would be fatal. They will maintain a technical existence at all costs. And ... the ability to transmit to Earth their independent views. Hence, with such a colony "on line", no Earth demagogue will be able to bamboozle the people into believing that freedom is slavery.
Herein lies the best reason for establishing a permanent independent colony on Mars. If people know it is there, they have reason to "look up" rather than down at the mud (where politicians dwell). These "Martians" will be real, free and independent and will become the benchmark for what can and should be achieved on Earth.
War of the Worlds
The first thing that such a colony should do is establish a high level of privacy. They will need "secrets" to keep from the Earthmen. In the event of disaster on Earth, they will be attacked. Saturn will devour his children.
This is inevitable.
The morbid philosophy of a decaying Earth will not abide a life sustaining philosophy that will be Mars. Hence, they must have hideouts ... places to go to weather the nuclear attacks from their planet of origin. Such attacks will peter out as the Earth loses its ability to send a warhead to Mars with pinpoint accuracy. Then they won't even be able to launch a rocket as the mind pool dries up.
But there will always be "secret" listeners. A signal from Mars will find its underground way to those who still thirst for a rational way of living. And there will always be millions of them.