Temporal Inertia
A favorite science fiction writer of mine from the late 80's postulated in his books about his theory of "temporal inertia". It was how he mitigated the effects of paradoxes.
Basically, he likened a time stream to a river with a strong current. Throw in a small stone and it will make a splash and a few ripples, but the current will quickly overcome the disturbance and in short order the course of the flow is restored. Larger and larger rocks will create larger and larger disturbances, but the current is strong enough to overcome all. Even a large boulder that sticks out above the surface creating a permanent change will still allow the river to flow around it, quickly reform, and continue on its previous course.
He did grant that if you were to drop a big enough boulder into the river, you will eventually change its course permanently.
If you think of a time line in this fashion, this temporal inertia would also tend to weaken the effects of butterflys.
Dave