Absolutely, God does pursue those who belong Him, but they can resist God. People can change, become unfaithful, start giving lip service, denying God, take the mark of the beast, etc. Of course God doesn't want that, but people can go astray. Jesus taught on this very matter, saying that sheep can go astray. While it's true the sheep who have gone astray are hunted down aggressively, there is still a possibility they can be lost.
Matt 13
12How think ye? if a man have an hundred sheep, and one of them be gone astray, doth he not leave the ninety and nine, and goeth into the mountains, and seeketh that which is gone astray?
13And
if so be that he find it, verily I say unto you, he rejoiceth more of that
sheep, than of the ninety and nine which went not astray.
14Even so it is not the will of your Father which is in heaven, that one of these little ones should perish.