Could there be a permanently manned Mars base before there is one on the Moon, or even in space (earth orbit) or even underneath the ocean on Earth?

I doubt it.

Just like the antarctic stations, they would be manned for a while and closed for another.

And, btw, why can't we just admit "Flags and footprints are OK"?

After all, they show what a country can do, it raises self-confidence, respect from the others, it is prestige AND most of all, it's exploration at its best!! It's curiosity for all the people back on earth who can share the event.

I'm much more for continuously exploring (moving on a planet, a moon or from planet or moon to planet or moon) than staying somewhere.
That way, the astronauts could leave lots of footprints in the solar system and will have to take a considerable number of flags with them!
They could even run short of them:-)

Raoul