One thing that often gets neglected in the conceptualization of how metabolism works with regard to insulin is the importance of activity in the whole scheme of things.
Blood Sugar Change = Food - Insulin - Activity
If Insulin + Activity > Food, you're going to drop. If you zero out Insulin (as some suggested by stalling your pump or not taking insulin immediately before) you only have to balance your food and activity.
What you need to do is figure out what the balance is for you. Figure out how your body responds to different stimuli and plan food and insulin according to your activity... not just overall, but over the course of your exercising. Just because you have enough food to keep your blood sugar change close to neutral in the first 5-15 minutes of exercising doesn't mean you have enough 30-60 minutes in.