If you use heavy picks (1mm, 2mm or thicker) strumming fast may cause the pick to go out of position, try different sizes for different styles of playing. For strumming chords try something with a little more flexibility, this way the fast strumming won't knock the pick out of position so much. But don't use a pick thats too thin, as you still want to give a little bit of attack and also control your dynamics and strumming volume.