I've never been totally stuck, but have stopped for some time usually to load or unload people in wheelchairs. Typically this happens everytime we ride HM, once in the part going backwards (rather uncomfortable!), but this trip we did not. It stopped during Journey of the Little Mermaid during the "Kiss the Girl" scene. It was funny because rather than an over the speaker announcement to stay seated and wait for the ride to begin again, the Sebastian in the scene stopped talking on script and gave the message to stay seated!