Thoughts which this brings to mind :
What insulin regime are you on? If MDI, there will be your basal still working.
Somehow you either need more food or less insulin. How to achieve that really depends on you - some will eat sugary things while exercising to keep a steady supply going, some will pre-load with food, some will lower their basal.
When you're dropping, do your legs feel it? My hypo awareness is quite good when exercising - my legs stop working
I'm getting better at checking for problems earlier though, also pre-loading - not to have my level high (though sometimes it is), but to have the food coming into effect while I'm out. I can generally do an hour on that. On longer things (the very occasional 2 hour run), I'll always eat half way round.
My annoyance is tweaking the basal has an effect for rather longer than the hour or so I want to take effect.