Those who believe with a living and saving, heart faith, their faith is unto righteousness (Romans 10:10, Matthew 5:6, Romans 5:19, 1 John 3:7) and also tenacious unto the enduring to the end (Hebrews 3:6, Hebrews 3:14, Matthew 10:22). They will never fall away from faith, for they are sealed by the Holy Spirit unto the day of redemption (Ephesians 1:13-14, 2 Corinthians 1:22, 2 Corinthians 5:5). The Holy Spirit seals faith into their heart that cannot be lost or taken away from them.
Those who have a mere mental assent to the tenets of the faith, or an emotional experience, who have a shallow, nominal, or lukewarm faith, are not sealed in this way. In fact, it is inevitable that they should fall away, because they are not of the good soil but are of the shallow or thorny ground.
Salvation is by grace through faith (Ephesians 2:8-9), and we have access by faith into this grace wherein we stand (Romans 5:1-2). Take away faith, there is no access to grace. And without grace, there is no salvation. So take away faith, there is no grace and thus, no salvation.
And yet eternal security is a reality in scripture. So I conclude that when we are sealed by the Holy Spirit, He places within us a righteous faith that will be in our hearts for ever. If someone falls away and loses faith, it is the evidence that they were not sealed by the Holy Spirit because their faith was not a living and saving, heart faith. I reject with my whole heart the idea that a man can fall away from faith and still be saved; for that is an unrighteous doctrine; and Jesus Christ, the author of the Bible, is the Righteous One (1 John 2:1).
And yes, mental assent to the doctrines of the faith is a requirement. However, mental assent to doctrine, alone, will not save the soul (see John 5:39-40, 1 Corinthians 8:1-3). And an emotional experience does not necessarily translate into a living and saving heart faith, either (Matthew 13:20, Mark 4:16, Luke 8:13); although one who is truly saved will very likely have an emotional response of falling head over heels in love with Jesus.