Many times different brands of paint and primer don't mix. Check out Home Depot and pick up some Rustoleum Painters Touch white primer. It's great.
Unfortunately for your helmet, there is hope so you don't have to sand and repaint the while thing. Sand it down with new sandpaper until your wet sanding with 800 grit. Then wash the helmet with dish soap and water, rinse it throughly. Then try and paint it. Sometimes the oils in our skin can transfer onto an object and will cause a paint to react too. Also when you paint the helmet use very light coats about 5 minutes apart. The lighter the coat the less time to react before it starts to dry.