It's not that they don't know that Jesus lives. It's that they no longer believe, for any variety of reasons.
Jesus even addressed the issue of ceasing to believe, in the parable of the soils. In Luke 8:13, He noted those who "believe for a while, and then in time of testing/temptation/etc, fall away". Yet, He never even suggested that they either weren't initially saved, or that they lost salvation. And in the previous verse, He noted WHY Satan steals the gospel; "lest they believe and be saved".
So it is clear from this any many other verses, that once a person believes in Christ, they are saved and sealed with the Holy Spirit, as God's own possession. Eph 1:13,14. For the day of redemption. Eph 4:30, 2 Cor 1:22 and 5:5.
This is probably one of the biggest Heresy's going around in these last Days.
Teaching that people who believe the Gospel, then turn away from Christ to serve other gods, which is clearly Idolatry, are still saved, would have to be the Mother of all Heresies, and is a slap in the face of all those who chose death as a martyr rather than renounce Jesus Christ as Lord.
This is exactly what Jesus taught about turning away is the face of persecution.
But the ones on the rock
are those who, when they hear, receive the word with joy; and these have no root,
who believe for a while and in time of temptation fall away. Luke 8:13
20 But he who received the seed on stony places, this is he who hears the word and
immediately receives it with joy; 21 yet he has no root in himself,
but endures only for a while. For when tribulation or persecution arises because of the word, immediately he stumbles.
Matthew 13:20-21
Jesus said plainly - 13 But
he who endures to the end shall be saved. 14 And this gospel of the kingdom will be preached in all the world
as a witness to all the nations, and then the end will come.
Matthew 24:13-14
The witness is: being killed for Jesus Christ as a martyr, during the great tribulation, just before Christ returns.
9 After these things I looked, and behold,
a great multitude which no one could number, of all nations, tribes, peoples, and tongues, standing before the throne and before the Lamb, clothed with white robes, with palm branches in their hands, 10 and crying out with a loud voice, saying, “Salvation
belongs to our God who sits on the throne, and to the Lamb!” 11 All the angels stood around the throne and the elders and the four living creatures, and fell on their faces before the throne and worshiped God, 12 saying:
“Amen! Blessing and glory and wisdom,
Thanksgiving and honor and power and might,
Be to our God forever and ever.
Amen.”
13 Then one of the elders answered, saying to me, “Who are these arrayed in white robes, and where did they come from?”
14 And I said to him, “Sir, you know.”
So he said to me, “
These are the ones who come out of the great tribulation, and washed their robes and made them white in the blood of the Lamb. Revelation 7:9-14
and again
Fifth Seal: The Cry of the Martyrs
9 When He opened the fifth seal, I saw under the altar the souls of those who had been slain for the word of God and for the testimony which they held.10 And they cried with a loud voice, saying, “How long, O Lord, holy and true, until You judge and avenge our blood on those who dwell on the earth?”11 Then a white robe was given to each of them; and it was said to them that they should rest a little while longer, until both
the number of their fellow servants and their brethren, who would be killed as they
were, was completed.
Revelation 6:9-11
JLB
Witness - Strong's 3142 -
martyrion
A Martyr is called a faithful witness.
This is the Christians testimony of Christ, to suffer death in the face of persecution, rather than turn away from Him.
Jesus is our example. Jesus is called the Faithful and true Witness.
10 Do not fear any of those things which you are about to suffer. Indeed, the devil is about to throw some of you into prison, that you may be tested, and you will have tribulation ten days. Be faithful until death, and I will give you the crown of life.
11 “He who has an ear, let him hear what the Spirit says to the churches. He who overcomes shall not be hurt by the second death.”’