How do those who believe in a pre-tribulation rapture explain that not everyone who remains will believe?
It is not only the failure to notice those disappearing in the rapture, other more significant events also fail to motivate people to repent.
Revelation 16:9-11 And men were scorched with great heat, and
blasphemed the name of God, which hath power over these plagues: and
they repented not to give him glory. And the fifth angel poured out
his vial upon the seat of the beast; and his kingdom was full of
darkness; and they gnawed their tongues for pain, And blasphemed the
God of heaven because of their pains and their sores, and repented not
of their deeds.
The rapture may occur coincident with or just prior to the events described in the first part of chapter six of Revelation where one out of every four people on earth dies. The rapture might not be discerned, but even if it was we have a picture of hardened hearts that would rather try to fight against God and endure unprecedented pain out of their hatred than chose a path of repentance.
There is also the possibility that their hardened hearts were sealed such that they have no interest in repentance.
2 Thessalonians 2:9-12 Even him, whose coming is after the working of
Satan with all power and signs and lying wonders, And with all
deceivableness of unrighteousness in them that perish; because they
received not the love of the truth, that they might be saved. And
for this cause God shall send them strong delusion, that they should
believe a lie: That they all might be damned who believed not the
truth, but had pleasure in unrighteousness.
There is an interesting line from the movie "The Maltese Falcon". Humphrey Bogart is toying with those trying to get information from him. His tactic is to exaggerate each scenario his inquisitors suggest so that they would have to kill him. He thinks that this effectively blocks their proposals. Sidney Greenstreet then urges caution, "Let's be careful because in the heat of the moment men are likely to forget in which direction their best interests lie".
While Greenstreet's warning does have truth in it, it fails to consider the obdurate. depraved, or reprobate mind. Men who have no interest in God when pressed by calamity will probably not make decisions based on even their own best interest, but simply vent their hate and frustration on others. We get a picture of this frustration when such men are not allowed to die.
Revelation 9:6 And in those days shall men seek death, and shall not
find it; and shall desire to die, and death shall flee from them.
The tribulation does an effective job of showing the heart of natural (fallen) man. We may deceive ourselves that we are evolving as a species and getting ever wiser, smarter, and more compassionate. However, unprecedented calamity and the righteous wrath of God will expose these delusions for what they are. Like Dorian Gray, we may have to face the ugliness of our real selves.