So, i've yet to not have this work, but i'd like some of you guys to give it a shot just to make sure i'm not crazy.
When catching a higher CP pokemon that you dont want to lose, throw your first pokeball. If it breaks out, run away, and tap on it again. Your first pokeball that you dont miss should work (at least i've had it work 100% of the time so far).Could definitely just be crazy rng, but who knows.
Obviously wont work if youre moving or in a car as you wont be able to tap the pokemon a second time if you run away.
-edit-
Apparently i was just having really good luck. Oh well!