The first way to approach this question is to look at the First Epistle of John as a whole, to see why it was written and whether there is a unity of structure.
Harold W. Attridge says, in 'Christianity from the Destruction of Jerusalem to Constantine’s Adoption of the New Religion: 70-312 CE', published in Christianity and Rabbinic Judaism:
A Parallel History of Their Origins and Early Development (edited by Hershel Shanks), page 172, that continuing friction among early Christians over the nature of Jesus is evident in the Johannine epistles. He says 1 John criticises ‘secessionists’ who departed in a dispute over the fleshly (human) character of Jesus (1 John 4:1-3) and the reality of sin (1 John 1:8-10).
Burton L. Mack says, in Who Wrote the New Testament, page 215, that a split took place in the Johannine community shortly after the turn of the second century. One faction thought it best to merge with other Christian groups of a more centrist leaning. Another party refused, holding to the enlightenment tradition of the community and developed in the direction of a Christian gnosticism. He says (page 218) the author of 1 John wanted to charge his opponents with being sinners (1 John 1:8-10), but since his new soteriology (doctrine of salvation) was about sin and forgiveness, the topic could backfire. He did not want to offer his opponents the promise of forgiveness. Mack calls the author's polemic against his erstwhile brothers and sisters vicious. Seen in this light, 1 John has a unity of purpose and a strong emotional content. When loyalty may have been fragile after such an acrimonious split, the frequent words of endearment might have been designed to draw the audience in to the author's story.
Raymond E. Brown says, in An Introduction to the New Testament, page 384, that the great majority of scholars think of unified composition and that a thesis of combined sources has little following. Looking, for example, at verses 2:1-6 as a separate composition, it has too little context and too little force to be a useful letter. On the other hand, verses 2:1ff seem to build on the argument about sin in chapter 1.