Is faith in Christ something you have forever or do you have to work at it every day to keep it strong?

Short Answer

From Protestant Reformed perspective, once you have a genuine saving faith (properly defined) you can never lose it. Either you have it or you don't. Our work doesn't contribute to it. The growth has to do with our love response to Jesus (see long answer below). Saving faith has to do with justification, not to be confused with other aspects of salvation: sanctification and perseverance.

Long Answer

faith is a vast topic, and Biblical references to it are numerous, linking it to many related concepts and doctrines. Not only that, faith is also central especially to Protestants, but leading to multiple opinions as well (example: Reformed vs. Wesleyan vs. Pentecostal). This answer is necessarily brief and introductory, restricted to your key concern about what part is constant, what part is changing, and what do we need to do to nurture the changing part.

I am answering from the Protestant Reformed perspective as represented by John Piper and GotQuestions website writers. Key positions in this answer are based on John Piper's three articles:

1. Can I Have Assurance Without Joy
2. Love Is the Main Thing In Saving Faith
3. The Agonizing Problem of the Assurance of Salvation

First, some key distinctions

1. I will focus on saving faith which every believer has for individual salvation, as opposed to spiritual gift of faith which the Holy Spirit gives in various measures for common good along with other spiritual gifts. Both are gifts, and we don't work for them. But spiritual gift of faith is a matter of degrees while saving faith is either you have it or you don't (binary states).

2. Saving faith has two aspects: intellectual assent and trust. Holy Spirit, who gives us this faith, enables us to say YES to certain facts about Jesus Christ as Savior and Lord (intellectual assent), as well as to TRUST the person of Jesus Christ as Savior and Lord. Many believers unfortunately only focus on facts about Jesus which the devil also know due to their spiritual nature. Only believers trust Jesus. Without trust, faith is not genuine.

3. Although saving faith has important role in Christian life (not just conversion), it is more prominently linked with justification, our imputed righteousness standing before God, which is either a "you have it" or "you don't have it" (binary states), not a matter of degrees. But sanctification IS a matter of degrees, although in Reformed theology it is still NOT our "work", but based on the Holy Spirit transforming our soul. Phil 2:12 about "working out salvation with fear and trembling" has to do with the sanctification stage (see GotQuestion.org article What does it mean to work out salvation with fear and trembling).

4. Saving faith can be genuine ("warranted resting") or self delusion ("unwarranted resting") (see article #3). It has to do with what we receive Jesus as. From article #2:

   the question is this: Receive him as what? It is possible that you see Jesus wrongly and receive him as what you see, and thus receive a Jesus who does not exist. For example, you may receive a Jesus who is not the divine Son of God. Or you may receive a Jesus who did not do miracles. Or a Jesus who did not rise from the dead, but is only a spirit and influence in the world. Or you may receive a Jesus who teaches that your reception of him is not his gift to you but yours to him.

   Most people who are self deluded is because they do not receive Jesus as "supreme treasure" (Matt 13:44). Genuine saving faith receives Jesus as personal Savior and Lord. It is STILL about either "you have it" or "you don't have it", so it is not as though you can work your way from self delusion to genuine (I used to struggle about this a LOT when I was younger). Warranted resting is based on "seeing the light of the gospel of the glory of Christ" which then enables us to rest on the objective warrant of the finished work of Christ on the cross while we are being sanctified subjectively. We either see it or we don't. From article #3:

   For faith to be real, there must be a supernatural “light” that God shines into the heart to show us that Christ is glorious and wonderful (2 Corinthians 4:6). This happens as a work of the Spirit of God through the preaching of the gospel.

   GotQuestions article What are some of the signs of genuine saving faith can help us distinguish whether we are deluding ourselves or not, by self examination.

5. Once we have it, saving faith DOES have its up and down, strong and weak (Rom 4:19-20), little or great (Matt 6:30, Matt 15:28), and its growth (2 Thess 1:3). It is very important to understand that this is NOT talking about justification. We are either saved or not saved. We are either united with Christ or we are not. We are either adopted or we are not. Even when we have a mustard seed faith it still means we are saved. The variability as to do with assurance which goes up and down with stronger and weaker saving faith. From article #1:

   Scriptures tell us to pursue full assurance, they are calling us to fight for growing faith in God, and for growing affections for God. Because they are the same fight.

6. In the Reformed tradition, scriptures that talk about guarding the faith does NOT imply that we can lose it. It is about the doctrine of perseverance which in the Reformed tradition the elect is guaranteed to be given sufficient grace to endure. Guarding has to do with dealing with demonic attacks, trials, and temptations. See GotQuestions article How can I keep the faith? In Reformed understanding, if a believer became an atheist later in their life, that means they never had a genuine saving faith to begin with.

What do we need to do to nurture the changing part of saving faith?

I wrote the previous section to isolate the changing part of 'saving faith' so we don't confuse the changing part with other things such as the spiritual gift of faith (distinction #1), sanctification stage (distinction #3), perseverance (distinction #6), etc. I also wrote the previous section so we are clear that saving faith is either "you have it" or "you don't have it" even though what we have maybe only a mustard seed (distinction #5).

So the remaining question becomes: what is it that is variable in saving faith and what we can do about it?

John Piper addresses this in article #2 linked above, based on a key understanding from Jonathan Edwards: Love is the main thing in saving faith. As pointed in distinction #2, genuine faith is trusting the person of Jesus, and trusting Jesus means loving Jesus as supreme treasure (distinction #4). The key verse is Matt 10:37:

I don’t think Jesus was teaching anything different from justification by faith when he said: “Whoever loves father or mother more than me is not worthy of me, and whoever loves son or daughter more than me is not worthy of me” (Matthew 10:37). And notice this love for Jesus that we must have is what you feel for your most precious family members.

John Piper distinguishes this love for Jesus (which is part of saving faith) from love for people (which is part of the fruit of faith):

Be careful. I’m not saying love for people is part of what faith is. That’s a fruit of faith. Paul says, “The aim of our charge is love [for people] that issues from . . . a sincere faith” (1 Timothy 1:5). But, yes, I am saying that love for Jesus is part of what faith is.

Does loving Jesus contaminate saving faith and turn faith into a performance, or a deed, or a work? John Piper address it this way:

It is right to jealously guard saving faith as fundamentally receiving, not giving. To be sure, faith is powerful in producing the fruit of deeds, but is not those deeds. Confusing a good tree with its good fruit makes Jesus’s words meaningless. “Every healthy tree bears good fruit” (Matthew 7:17). So I want to be vigilant to guard faith as essentially receiving, not performing or giving.

What is this experience of loving Jesus that can grow? As in all loving, there is growth involved in which John Piper terms "spiritual affections":

think that for trust in Jesus to be authentic trust, it has to involve spiritual affections for Jesus. For example, I think that saving trust has to be thankful trust, and admiring trust, and treasuring trust, and pleased trust. In other words, if you say you have saving trust in Jesus, but you don’t experience Jesus as the most desirable, admirable, valuable, enjoyable person in your life, you should question whether you have true saving faith.

CONCLUSION: What we can do to grow our saving faith is to grow our spiritual affections to Jesus, grow our love for Jesus as being more aware of receiving Him as supreme treasure:

This does not mean “Do things for him.” It means “Feel things for him.” Treasure him above all else. Be satisfied in all that God is for us in him.