It is possible to have something called 'reactive hypoglycaemia', where the pancreas overreacts to an increase in glucose and puts out more insulin than is required to bring the level back to normal, with a subsequent drop below normal. I believe that, for an untreated Type 2 where levels are swinging, the pancreas can lose the fine control necessary. (Put in my half-remembered layman non-doctor terms!) 🙂
Thanks. That's the bit I was missing! 🙂