We must firstly clarify that HPV treatment is not causal. There is no medicine that can completely eliminate the virus from our body. What we call treatment is the removal or destruction of the inflamed tissue. The virus remains on the epithelia of the genital system for a long time or even forever, but this is not a cause for concern, even in cases of infection by high-risk HPV types. Recurrences of lesions are rare, and if patients are monitored (tested with Pap test or HPV test) there is no risk of losing a precancerous lesion.
In the majority of cases the immune system prevails and the inflammation regresses spontaneously, and we do not have any recurrences. In other patients where intervention is required to destroy or remove the lesions (genital warts or premalignant lesions), we again expect the immune system to prevail and suppress the activity of the remaining viruses. After the lesions are gone our body has a smaller viral load to deal with, making suppression of the remaining HPVs easier.