This happened to me at least 3 times, twice during "Together We Stand" (main scenario quest) after a battle.
Changing equipment, everything didn't help.
I tried to run to the goal at a snail's pace and failed the quest.
Then when it happened again I realized active mode's speed was still normal, and finished the quest.

Whenever this happened the only way for me to fix it was to relog.
I don't know if it's related, but I'm using a PS3 controller to play.