In JSRF there's a movement mechanic called dashing - if the thumbstick is neutral and you press it in a direction quickly enough, your character will have slightly faster acceleration, and there will also be a dashing animation as well as black speed lines visible around the character.
However, on every dash attempt, there is a chance that the dash will not work, even if you move the thumbstick with the appropriate speed. Another thing is that eventually, dashing will cease to function altogether, no matter how fast or hard you move the stick. Neither of these things have an explanation as to why they happen.
For some bewildering reason, unplugging and replugging your control fixes your dashes, at least until they stop working again. It also seems to mildly affect your directional angles for a few seconds - i.e. 'straight' may feel like 'straight and a tiny bit left'. The safest place to replug is during cutscenes, any other place will pause the game until you replug your controller.
This does not seem to happen on emulator, which may indicate that this is a problem with original Xbox hardware.