Do Evangelicals think you have to be saved every day?

There are a couple of different tacks to take on this, in addition to the other answers given

A belief in lost salvation

Not all Christians believe in "Once saved, always saved". In fact, that's a fairly large theological divide. I could see your relative thinking that this is the case and having a "daily salvation" doctrine as a bulwark against it. I have never seen any mainline denomination that believes in lost salvation preach this sort of doctrine, however.

Do it harder so it sticks

Some people don't rest in doctrines like "my grace is sufficient for you" (2 Cor 12:9), so they overcompensate by trying to "out-Christian" everything. They make everything under the sun about Jesus, Christianity, etc. Thus, in their minds, we might need to be saved every day, because lesser Christians might slip up and lose theirs.

Again, no mainline Christian denomination teaches such a thing.

OP: Are evangelicals supposed to be saved every day or more than 1 time a day?

How can one be born again and again and again? Evangelicals understand that a person is born again, one time, forever. They would follow Jesus Christ.

Jesus answered and said unto him, Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God. John 3:3

Even unbelievers understand Jesus met born again once.

Nicodemus saith unto him, How can a man be born when he is old? can he enter the second time into his mother's womb, and be born? John 3:4

Born again once, not reentering the womb a second, third, or fourth time.

Here is Peter on the issue.

Being born again, not of corruptible seed, but of incorruptible, by the word of God, which liveth and abideth for ever. ... But the word of the Lord endureth for ever. And this is the word which by the gospel is preached unto you. 1 Peter 1:23, 25

To be sure, there are some religions and cults who teach that you must be saved over and over, but not evangelicals. Perhaps the OP should take a closer look at the pamphlet presented.

In my answer to this 2019 Stack question, I include a link to another, related, question, and both of those might provide you with some useful information on the topic of saying what has come to be known as "the Sinner's Prayer", to know that one is 'saved'. What is the biblical basis for “the Sinner’s Prayer” and do Protestants believe that saying the prayer make one a Christian?

The simple answer is, "No, Evangelicals do not think you have to saved every day'.

Answers have already been given as to what the biblical doctrine on being saved is (and is not) so I won't repeat that. By way of conclusion, I want to raise a possibility that might account for unwarranted repetition of an insistence that people keep repeating such a prayer every day.

This is actually the far swing of the pendulum on this topic. It is quite extreme. The usual reaction is to believe that such a prayer only has to be repeated once, and then it can be (basically) forgotten about. A common Evangelical stance is that saying 'the Sinner's Prayer' is key to salvation and 'does the trick' (to put it crudely). Very many Christians are alarmed at that particular Evangelical view, by the way, and much literature has been written exposing what they see as the error of it. However, you do not ask about that. Many Evangelicals, when asked if they are 'born again', cheerfully say, "Oh yes. On [such-and-such a date], I said the Sinner's Prayer, so I'm saved." They might not always remember the exact date, but they usually tell you the location - some big Rally, or in a particular church - occasionally just at home.

That is the usual view, and it is quite opposite to your brother-in-law's view. According to the limited information you have provided, he comes across as obsessive about this, and getting more so as he gets older, perhaps? It may indicate a real insecurity regarding yourself and your offspring, worrying in case what you've said before might not be right, or even that his memory is failing. That he should require such persistent reassurance is most unusual but, really, you don't have to convince anyone on that score, if you know you are, indeed, a Christian.

As Nigel J has made clear, Evangelical Christians do not believe a person has to be saved every single day. When we repent before God and turn to Him, placing our faith in what He has done in Christ Jesus, forgiveness for all past sins is immediately forthcoming. It is God’s free gift. At that moment in time, it is Jesus who accepts us, and He will never lose any that God has given to Him.

Here are some Bible verses to encourage and uplift you:

I have been saved – in the past – from the penalty of sin – by a crucified Saviour: “For in this hope we were saved" (Romans 8:24). “For it is by grace you have been saved, through faith – and this not from yourselves, it is the gift of God” (Romans 2:8).

I am being saved – in the present – from the power of sin – by a living Saviour: "For the message of the cross is foolishness to those who are perishing, but to us who are being saved it is the power of God" (1 Corinthians 1:18).

I shall be saved – in the future – from the presence of sin – by a coming Saviour: "Since we have now been justified by his blood, how much more shall we be saved from God's wrath through him!" (Romans 5:9)

In the past, God granted us justification, a once-for-all, positional holiness in Christ. Now, God guides us to maturity, a practical, progressive holiness. In the future, God will give us glorification, a permanent, ultimate holiness. These three phases of sanctification separate the believer from the penalty of sin (justification), the power of sin (maturity), and the presence of sin (glorification). https://www.gotquestions.org/sanctification.html

God is love, and God is gracious. We can rely on His word and in His promises. The truth sets us free, free from bondage to legalism and to the dictates of men who might seek to control and manipulate others. We answer only to God and not to any man. Take heart! You are loved with an everlasting love (Jeremiah 31:3).

Please note, however, that God's everlasting love is not universal - it's for those who have come to saving faith, people like you and me.

It is true that many scriptures exhort us to spiritual exercises on a daily basis : prayer, worship and the care of our fellow human beings.

And it is true that Jesus Christ himself exhorts to continued and increased devotion and maturity in the faith. I am thinking, here, of the seven letters written to seven churches which express deep concern for the daily walk and pilgrimage of every member of the body of Christ.

But no scripture I can think of and no group or gathering I have ever come into contact with, in the past fifty five years of my own Christian profession (I am in my seventies) has ever expressed the need of being 'saved every day' nor have I ever read, in Church history, of such a doctrine.

This undermines the work of God in the soul. It undermines justification by faith, which is God's work (to justify) and the Holy Spirit's work (to bring to repentance and to faith).

We are not saved by works, by decisions, by assertions, by acceptances nor by commitments or promises or oaths or covenants of our own.

... For by grace are ye saved through faith; and that not of yourselves: it is the gift of God: [Ephesians 2:8 KJV]

Those who have repented, who have believed the gospel of Jesus Christ, the Son of God, who have been publicly baptised, and who 'continue in the apostles' doctrine and fellowship and in breaking of bread and prayers', Acts 2:42, have ' already been delivered from the wrath to come' , 1 Thessalonians 1:10, and we look, in hope and in love, for his promised return.

I was baptised into the presbyterian Church of Scotland at the age of five (I remember the event) and I volunteered for baptism, again, as an adult, at the age of sixteen, into the Baptist Assembly of Scotland. I am now independent of any denomination.

My evangelical testimony, written at the age of twenty-one in 1972 (and published in 1992) is freely available on my website. See my profile for the website details.