Just like the best time to escape a pin is when someone first puts you in it, the best time to get out of a submission attempt is at the beginning. The longer you wait, the more time they have to get all of the details set. Just because something isn't working at first, it doesn't mean that it never will. Waiting to try to get out until a submission attempt is truly threatening you is waiting far too long.
On the flip side, I also used to give up on submissions too soon. Instead of keeping hold of it and adjusting, I would completely let go, and then have to start from scratch. There's no reason to do that, as long as you are not putting all of your energy into it. You should be able to relax and not wear yourself out while holding a sub attempt, as you work toward perfecting it. Conan likes to tell us to think about how our partner is feeling at times like these. We've all been there, so we know how demoralizing it can be. If you can hold that submission longer than they can stand being in it, then you win. If you tire yourself out by trying to finish it before it's really set, and give up before they do, then you lose.
I think it all goes back to "Never Surrender". Never be complacent about being in a sub that isn't working, and never give up on doing one that could be successful if you're patient. Never stop insisting on getting what you want.
"Hey baby, there ain't no easy way out. I'll stand my ground, and I won't back down."