The hubsan X4 has 2 or 3 flight rate modes...Low and high...The button on the very top left of the controller changes the rate....The x4 needs to be in high rate which should give you either 2 or 3 beeps when its pressed...Now the quad needs to be on as level a surface as possible then calibrate the gyros by moving the right stick back and forth from left to right quickly until the quad lights blink...If you press the button and hear one beep its in low..2 beeps is either med rate or high and 3 would certainly be high..if you hear 2 then press it again and hear one beep then 2 beeps is high rate.
Its been a while since ive done this with my x4 but you can find videos on youtube on how to re calibrate the x4, not re bind as you may have been doing and thinking it was re calibration...Re calibration should take care of those issues you are having.
Simple small crashes and less than easy landings can throw out the gyros often...I usually just do a re calibration before every flight and if i crash, do it again as needed...Its typical behavior of the toy gyros so, its normal for a quad to act funny sometimes.
Just so you are aware, in high rates the x4 will be a different animal so be ready
...You can switch back to low rates after you re calibrate if you like by pressing the same button until you hear one beep.
I think youll be up and running again and back to the fun when you do the proper procedure to re calibrate...Let us know how it works out.