The economy went from 0% growth for 100s of years to 3% growth that lasted many hundreds of years.

Yes, at each step keeping the 3% growth needed things to keep going, but the big thing was unleashing the nonzero growth rate, to get unstuck from the local minimum.

What makes that a rule? Can causal chains not last more than X amount of time? What is the cutoff?

A small increase in exponential growth will have a huge effect after 400 years