What is the biblical basis for the doctrine that salvation can be lost?

yes it is possible to be in a state where you cannot be forgiven and logically if you cannot be forgiven then you cannot be saved. Jesus said that.

"All sins will be forgiven the sons of men , those who blaspheme against the Father will be forgiven, even those who blaspheme against the Son or the Christ will be forgiven but those who blaspheme against the Holy Spirit will not be forgiven".

If you cannot be forgiven blasphemy against the Holy Spirit then you are irredeemable because of the doctrine that

Blaspheming against the Holy Spirit makes one guilty of an eternal sin

There is a reason why Jesus asked Christians to pray for forgiveness of their sins in the Lord's prayer because it is impossible in the human state to not sin with free will. The Bible encourages repentance and encourages Christians to pray for forgiveness of their sins from God. I do not think Christians who are saved are capable of blasphemy against the Holy Spirit which is the only thing that can make one guilty of an eternal sin so no there is no other sin or thing that can make a Christian irredeemable.

TL;DR: Paradoxically, that it is impossible to lose one's salvation is a belief supported by both sides of the issue.

One can clearly fail to receive God's promise:

For whoever gives you a cup of water to drink in My name, because you belong to Christ, assuredly, I say to you, he will by no means lose his reward.
— Mark 9:41

Look to yourselves, that we do not lose those things we worked for, but that we may receive a full reward.
— 2 John 1:8

“Behold, I am coming quickly! Hold fast what you have, that no one may take your crown.
— Revelation 3:11

But once one has received salvation, it will not be taken back:

And I give them eternal life, and they shall never perish; neither shall anyone snatch them out of My hand.
— John 10:28

There shall be no night there: They need no lamp nor light of the sun, for the Lord God gives them light. And they shall reign forever and ever.
— Revelation 22:5

The difference in doctrine results from the understanding of when one receives salvation.

The once-saved-always-saved people believe that salvation occurs when one is "born again" at baptism and the reception of God's holy spirit.

The above, and other similar scriptures, are simply examples of people that were never truly saved in the first place, and who only thought they were saved, or even pretended to be saved.

The apparent "loss of salvation" is simply an obvious sign of something that was inevitable for such people; they were not among those that had received salvation. Those that are truly saved will not exhibit such behaviour.

Other denominations believe that salvation is not received until Christ's return, at which time the saved are converted into immortal spirit beings:

in a moment, in the twinkling of an eye, at the last trumpet. For the trumpet will sound, and the dead will be raised incorruptible, and we shall be changed.
— 1 Corinthians 15:52

It is then that the combined human and divine spirit, which has been developing within each true Christian since Baptism, is "born again":

Jesus answered and said to him, “Most assuredly, I say to you, unless one is born again, he cannot see the kingdom of God.” … That which is born of the flesh is flesh, and that which is born of the Spirit is spirit. … The wind blows where it wishes, and you hear the sound of it, but cannot tell where it comes from and where it goes. So is everyone who is born of the Spirit.
— John 3:3,6,8

Being "born again" does give one immortality and salvation, but that final process happens when Jesus returns, not during baptism.

Being a true Christian isn't enough though. Receiving God's holy spirit at baptism is necessary for salvation, but it is by no means sufficient.

Occasional slips, even involving serious sins, are possible, but one must continue strengthening one's character right up until the end (either one's death, or Christ's return):

For you have need of endurance, so that after you have done the will of God, you may receive the promise
— Hebrews 10:36

And you will be hated by all for My name’s sake. But he who endures to the end will be saved.
— Matthew 10:22, Mark 13:13

but Christ as a Son over His own house, whose house we are if we hold fast the confidence and the rejoicing of the hope firm to the end.
— Hebrews 3:6

For we have become partakers of Christ if we hold the beginning of our confidence steadfast to the end
— Hebrews 3:14

And he who overcomes, and keeps My works until the end, to him I will give power over the nations
— Revelation 2:26

Paul himself had no doubt that he was a baptised Christian, that he carried God's holy spirit within him, or that it was his purpose in life to perfect his character. But even he had concerns about the possible result of failing his duty as a Christian:

But I discipline my body and bring it into subjection, lest, when I have preached to others, I myself should become disqualified.
— 1 Corinthians 9:27

Those who believe Christ have passed into eternal life, are living it:

Luke 10:17 NET Then the seventy-two returned with joy, saying, “Lord, even the demons submit to us in your name!”

Their names are written in the book of life

Luke 10:20 NET Nevertheless, do not rejoice that the spirits submit to you, but rejoice that your names stand written in heaven.”

They are enlightened about the process:

John 12:24 NET I tell you the solemn truth, unless a kernel of wheat falls into the ground and dies, it remains by itself alone. But if it dies, it produces much grain.

Some find new teachings hard to accept:

John 6:53-60 NET Jesus said to them, “I tell you the solemn truth, unless you eat the flesh of the Son of Man and drink his blood, you have no life in yourselves. The one who eats my flesh and drinks my blood has eternal life, and I will raise him up on the last day. For my flesh is true food, and my blood is true drink. The one who eats my flesh and drinks my blood resides in me, and I in him. Just as the living Father sent me, and I live because of the Father, so the one who consumes me will live because of me. This is the bread that came down from heaven; it is not like the bread your ancestors ate, but then later died. The one who eats this bread will live forever.” Jesus said these things while he was teaching in the synagogue in Capernaum. Then many of his disciples, when they heard these things, said, “This is a difficult saying! Who can understand it?”

He is referring to the teaching that one needs to abandon the idols of Egypt/the world, which are basically vending machines (they served men!), and not replace them with newer vending machines, but with a God who taught servanthood.

Instead of persevering and finding out what it involved, some quit:

John 6:66 NET After this many of his disciples quit following him and did not accompany him any longer.

Belief is what gets your name into the book of life. Unbelief gets it blotted out:

Revelation 3:3-5 NET Therefore, remember what you received and heard, and obey it, and repent. If you do not wake up, I will come like a thief, and you will never know at what hour I will come against you. But you have a few individuals in Sardis who have not stained their clothes, and they will walk with me dressed in white, because they are worthy. The one who conquers will be dressed like them in white clothing, and I will never erase his name from the book of life, but will declare his name before my Father and before his angels.

The thief on the cross next to Jesus believed. That is what counts, being conquerors at the point in life you are in. Not the progress made, nor how mature you have grown (and cynical).