Not enough atmosphere to generate lift. Same reason we can't fly satellites into orbit.
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Silly question, but why is it that we can't fly a satellite into the orbit of Mars? What is it about the space 300 miles up from Earth that differs from Mars? (unless we also want to discuss geosynchronous orbit)
Edit: I should have written "launch" a satellite into Orbit from Earth to Mars
Orbit isn't about going up - it's about going sideways so fast that the planet curves away just as fast as you fall towards it. While you can use the atmosphere to lift yourself up to a certain extent, it doesn't help you achieve orbit. The 100km boundary for space on Earth isn't picked as just a clean number - it's the altitude at which a plane would have to fly at orbital speeds to generate the required lift, and if you're going orbital speeds you don't need lift.
I know this doesn't exactly answer your question, but it might help to frame it better.
I probably should have phrased it better, actually. I understand the concept that the satellites are falling along a path in orbit that causes them to "miss" the planet as you describe. I misunderstood the parent's phrasing use of flying, which implies the presence of an atmosphere, as opposed to just "putting" a satellite into Mars orbit(by way of launching a rocket with the desired payload or whatever).
Actually we currently have 3 satellites orbiting Mars:
http://en.m.wikipedia.org/wiki/Category:Artificial_satellite...
"Same reason we can't fly satellites into orbit [of Earth]"
The pressure on the surface of Mars (0.6 kilopascals or 0.087 psi) is about one tenth of the pressure at the height of 20KM from surface of Earth (Armstrong limit 6.25 kilopascals or 0.906 psi). Of course, the structure of the "Martian" plane has to be designed accordingly. But definitely not impossible though.
Why not a drone dirigible?
My hypothesis: The minimum atmosphere likely makes it hard for anything to fly close to the surface. Most of our drones/flying machines (winged or rotored) depend on there being relatively thick air to "push" off of.