I frequently suspend my basal (stop my pump) when exercising.
The thing I find is that I have to time the suspension appropriately.
As we know we pre-bolusing (and it uses the same insulin on a pump), insulin can take 30 minutes or so to start working. Therefore, I have to time my basal suspension for 30 minutes before starting the exercise and to finish 30 minutes before finishing. If I don't resume basal early enough, my levels will go high as soon as I finish exercise.
If you suspend basal when you are already hypo, it is too late (unless you have a lot of insulin onboard).