Its definitely not heat damage. Its just what straight hair does. This is why you hear people with naturally straight hair constantly complaining they can't do anything with their hair ( makes me very grateful for the super versatile hair I have). IMO If your hair isn't moving, its probably lacking elasticity and moisture. It should be falling.
That said now we need to figure out how to get your curls to stay! I too only have a limited amount of time with curls when my hair is straight, especially in the hot humid summer, unless I use so much hairspray my hair is hard-- then it doesn't move at all.
What I recommend if you want to have curls that last longer than 20 minutes/ 1 hour is rolling your hair over night then applying some (not a lot of) hairspray in the morning before you take the rollers down, and also spray them quickly right when you take them down. The hot iron is really like an in case of emergency thing, I cringe every time i curl my ends, because I am always afraid I will *** them up in the process.
Another idea is to actually rollerset your hair so it initially dries into the curl form, ( rather than being straight hair that is now going to be curled) and then blow out and or flat iron the roots. That should look pretty nice considering you are about BSB/BSL
I've also heard great things about carusos but I don't have them.
Lastly, I think the culprit is most likely the summer heat and humidity. I have the same kind of thing happen that many of you described, straight-curl-frizz, all within 20-40 minutes. You might have better luck when things cool down
Hope that helps!