It's written to "you who believe in the name of the Son of God". That is who may know that they have eternal life, not the person who has turned back to unbelief. As John himself says in this very letter, the condition for having eternal life is that the word remain in you:
"23Whoever denies the Son does not have the Father, but whoever confesses the Son has the Father as well.24As for you, let what you have heard from the beginning remain in you. If it does, you will also remain in the Son and in the Father. 25And this is the promise that He Himself made to us: eternal life." 1 John 2:23-25
Some will argue that the word will always remain in the believer (that is, they will always believe). Fine. But that doesn't change the condition for remaining in the Son, the Father, and the promise of eternal life. You must continue in your believing all the way to the end to be saved in the end:
"6 ...we are His (God's) house, if we hold firmly to our confidence and the hope of which we boast." Hebrews 3:6