Common wisdom has been that the vast majority of HPV infections clear within a couple of years, and that once they are gone they are gone - any new virus found later in life is caused by a new infection. However, a paper recently published in the Journal of Infectious Disease suggests that may not be the case. They performed an analysis of age-specific HPV rates in the population and determined that they would likely be best explained by an age-related reactivation of the virus in older women.
That said, it's important to note that they study investigators did not actually witness any reactivation of HPV. They performed a cross-sectional study and an intense data analysis to explain age trends, which is fascinating but very different than actually witnessing reactivation in a population of women. Therefore, I think it's very important to treat this result as preliminary. It may turn out that age-related reactivation of HPV explains some of the viral prevalence in older women, but until that has been observed directly, I think it's too early to say.