Does God sometimes stop talking (striving) with men who reject Him?

In Genesis 6:3, “The Lord said, My Spirit shall not always strive With man.”

Did this apply only to that dispensation?

The words in question are in close connection with the intermarriage of “the Sons of God” and “the daughters of men,” described in Genesis 6, by which the barrier between the Seth line and the descendants of Cain was broken down. The sons of God did not make the worldly women godly, but the reverse process took place, as is nearly always the case to-day under similar circumstances. A great increase of evil was the result, and the world was filled with violence and corruption. This was foreseen by God, Who gave utterance to the above solemn declaration, adding, “for that he also is flesh.” Man had had at least two thousand years to show what “evolution” could do, if such a principle existed. Surely he would have developed into something supremely excellent. Let verse 11 reply: “The earth also was corrupt before God and the earth was filled with violence.” Is not such a development more consistent with the doctrine of the fall of man, than of his constant and consistent “evolution” toward a higher ideal? We need not be surprised if the Modernists wish to expunge the first ten chapters of Genesis. To believe in the evolutionary hypothesis one must not only deny the plain statements of Scripture, but shut one’s eyes to the facts of history and human experience. However, God adds in grace, “Yet his days shall be an hundred and twenty years”; that is, I take it, there was to be still a respite of that duration.

There is no evidence to show that the testimony of Noah, the “preacher of righteousness” ceased before the flood. But as far as I know, God nowhere pledges Himself to continue pleading with men till the end of their careers. Indeed, such emphasis is laid on immediate decision, that it would be the height of folly to count on even one more chance. We know that when the Man of Sin will be revealed God will send on those, who will have refused the truth, a “strong delusion that they may believe the lie” (2 Thessalonains 2:10-12). This moment however has not yet arrived, and it would be both unprofitable and presumptuous to attempt to show that the Spirit has ceased to strive with anyone still alive, for this is to invade the divine prerogative, and pretend to “search the heart.”