Plane gets damaged while flying, what am I doing wrong

I've successfully stolen a small plane from the LS-airport and managed to take off with it.
But after just a few miles, the engines start to degrade, black smoke appeared and I eventually lost height and crashed.

The plane was of course shot at while still on the runway, but only slightly damaged. I don't think a police helicopter could have followed the jet plane for long and I didn't hear further gunshots while flying.

What did I do wrong? Am I not supposed to fly early in the game? Do I need to manually retract the landing gears? Do police helicopters have a really long (and silent) weapons range?