What you are talking about is directly linked to (and answered by) the epidemiology of an infection (or a disease). That is your magic word. A quick lesson on how to search through the internet:
Open up the Wikipedia entry on HPV infection, and go to the Epidemiology section, specifically for the United States: HPV Infection Epidemiology for the US.
Search for pertinent information, such as the following:
The prevalence for high-risk and low-risk types is roughly similar over time. 
Check the following graphic, that accompanies that part of the article:
See the  number, that is a reference. You can click the number and it takes you to the reference:
Dunne EF, Unger ER, Sternberg M, McQuillan G, Swan DC, Patel SS, Markowitz LE (February 2007). "Prevalence of HPV infection among females in the United States". JAMA. 297 (8): 813–9. doi:10.1001/jama.297.8.813. PMID 17327523.
If you click on the name of the article, it takes you to the corresponding article on the journal website. You can read what the situation was like in 2007, the article is open, by the way.
So, the highest prevalence, even over 40% was detected in women between 20 and 24 years of age. That could be what you might have read.
You say that the virus is naturally cleared within 2 years, let's fact-check that. Here is what the CDC tells us:
Treatment is directed to the macroscopic (e.g., genital warts) or pathologic precancerous lesions caused by HPV. Subclinical genital HPV infection typically clears spontaneously; therefore, specific antiviral therapy is not recommended to eradicate HPV infection. Precancerous lesions are detected through cervical cancer screening; HPV-related precancer should be managed on the basis of existing guidance (see Cervical Cancer).
The CDC fact sheet, also states:
In most cases (9 out of 10), HPV goes away on its own within two years without health problems. But when HPV does not go away, it can cause health problems like genital warts and cancer.
OK, so you are correct, most cases are cleared within two years.
So this is the prior research (maybe I should edit all this stuff into the question). Now, the answer to your question:
While the immune system is fighting to clear the virus, individuals keep spreading it to others. It's that simple. Before clearing the virus, one individual may infect a large number of other individuals, so the numbers of current infections are kept way above zero, just by virtue of that. The prevalence appears to drop in older ages, potentially because people don't have sex as much, so the rate of new infections drops significantly, or they have cleared the infections naturally and are invested in monogamous relationships, so, again, the rate of new infections drops significantly.
There really is nothing more to that, it's a complex equilibrium between how many people are newly infected, versus how many people clear the infection at any given time. The complicated dynamics (there is a large number of parameters at play, but it doesn't matter for the answer to your question) seem to lead to a balance, which is about 26.8% of women infected at any given time, in the US, in 2007, at least in a relatively representative sample.