..check your equipment screen - perhaps the thruster was damaged, and so unable to fire? If this is the case, then this damage is manageable by rotating 180° and using the opposite, working thruster, with FA-on or off, and avoid relying on AP until you've made repairs (in principle, you can fly an entire mission, from launch to landing and completing any objectives en route, using just FA-off with only a single working thruster.. just a question of having the 'right stuff')..
Alternatively, if you're playing the original FFE then perhaps it's the 'velocity fudge' feature/bug - this can suddenly slam you into terrain seemingly randomly, even though your ship's in perfect working order. In any event, with the time and effort involved in getting DOSbox up and running, you'd be much better off installing the latest version of FFED3DAJ, which allows you to disable this particular 'feature' in the .cfg, as well as enabling a host of really useful other ones.
Do stick with it though! If you got this far, you must already have noticed this is an infinitely better game than ED.. the sense of achievement of every flight is a big part of that; the core experience that ED cheapens to total gaming bankruptcy, here, it's you vs the elements, playing the causal and deterministic against the random and procedural, it's the difference between rFactor 2 and Pole Position, realism instead of canned FX (especially with FD's velocity fudge disabled).
Best advice is to use the latest FFED3D build, disable the velocity fudge in the config, map all your thrusters to a familiar key cluster (WASD, Lshift & Lctrl, Q & E for roll, or whatever), check your equipment status screen in the event of a thruster problem, maybe also a visual inspection from external view (if all thruster anims are enabled for your ship - some aren't), and learn to compensate and manage damage... flying FA-off for long distances is largely a matter of learning which speeds are manageable at which ranges for a given thruster power - generally you don't wanna be much more than 200 kms as a planet looms into visual range, and 30 kms before touching atmosphere - whatever the range to a target, divide that number by two then apply max thrust towards it until halfway there, then spin it round and continue applying max thrust in reverse for a smooth arrival. So long as you have a single working thruster anywhere on your ship, you can bring it home..