On Earth too, it's magnetic field is really weak.
Mars, IIRC, has none.
To my understanding, Mars does not have an active core - it's kind of... dead in a sense. Thus, this is the reason it does not have a very coherent magnetic field. But, it does have magnetic
fields, they're just patchy, and as you said, weak.
Battuta, here's an interesting idea, though it might be difficult to implement. Could you make the gravity script trigger for a ship that looses its engine subsystem(s)? That might make for a really neat dynamic in the atmosphere - if you can take out his/her engines, they're just as dead as if you beat their hull to pieces.