I had Super Speed and Speed Phase active when I entered a lower level AE mission. I lost Super Speed when I entered the mission, but Speed Phase stayed on. I could run through NPCs and was flagged as Only Affecting Self until I was attacked, then I could fight back. The Speed Phase icon was ghosted in a power tray and I couldn't turn it off, but it was still running.
When I quit and went back to 50, Speed Phase was still running and ghosted. I had to turn Super Speed on and off again.