Is there anyway to skip this bullshit? I already calibrated joystick, but every time I start the game it prompts me to calibrate joystick. It is not only thing. Unfortunately half of the times or even more my joystick is not working so I need to restart it and when I am able to skip it with clicks I calibrate it in game with Alt-C, but than after restart it's same shit again.

The dos X-wing and Tie Fighter games didn't save your calibration.

What joystick do you have?
All the joysticks I had always worked under dosbox.

It works. Just a couple of times it did not. And the joystick is Logitech Attack 3 Joystick.

Well, it should be more than fine, probably some problem with contacts?
Also keep in mind that due to a quirk of the engine you cannot point at certain parts of the skybox and if you try the stick will act all jittery, it's really a pain when the enemy fighter you are tailing happens to pass through the wrong part of the skybox but it's a transitory thing so no need to recalibrate.

You are forced to calibrate every time at launch because of another limit of the DOS game engine (most games were like that, the few games that weren't had very rough stick movements), the windows games (XvT XWA and the remakes of the first two) of course don't have this problem as they use DirectInput.