How do you know this, for a fact? The planet Earth could remain "lucky" for the rest of the life of the solar system.
Remain lucky? You've got to be kidding. The Earth has never been lucky. Giant space rocks have been hitting the Earth on a regular basis since it came into existence. What makes you think that will somehow magically change? Have we run out of asteroids already? The chance that the Earth will never again be hit by a large extraterrestrial body is so infinitesimal, that for all practical purposes it is zero.
So yes, it is inevitable that another giant space rock is going to fall out of the sky at some point.
Knowing of the risk of an asteroid impact during the 1600s, would you ask that they devote considerable resources to prevention?
What do you mean by "considerable"? Would 1% of one year's worth of the world's economic output in the 1600s be "considerable" in your mind? Does 1% meet your definition of "massive amounts of resources"?
Today, Gross World Product is currently around 75 trillion dollars per year. Let's say the cost to build and test an asteroid defense system is two billion dollars over ten years, or two hundred million dollars per year. Two hundred million dollars is what, 0.0002857% of yearly GWP? Have I got that right? Someone better check my math on that.
Assuming my math is correct, do you really think 0.0002857% of the world's economy for ten years would be so damaging that it would cause hardship for...well, anyone?