With my limited knowledge, I understand that the vaccine works by inserting fake HPV-like material in the body, thus inducing the immune system to build up defenses against it, so when the body is exposed to real HPV on the wild the immune system will be able to handle it.
That makes sense, however, why can't the body still build up the defenses when there was already an exposure? Specially when the HPV virus is "dormant" and undetectable.
EDIT: After the discussion with @Bob in the comments section below, the hypothesis is:
In an infected person whose immune system was able to clear the acute infection, the virus (single infected cells) is constantly trying to enter lytic cycle again, only to be defeated by the immune system (because one infected cell leaving dormant state alone might not be effective); and then when the immune system is compromised for some reason, the virus is successful into entering lytic cycle and then there is a new clinical infection.
If this is all truth, then the answer to the question is that the vaccine does "work" in the sense that the body still reacts correctly (by responding to the antigen) to it, but it is, in practice, useless because: 1) when the virus is dormant there isn't anything for the immune system to do; 2) when the virus strikes, the immune system was already exposed to it anyway, so it is generally able to fight and there is no need for the vaccine; 3) the infection will get clinical again only when the immune system is, for some reason, defective.
The whole point of the vaccine is to never let the virus infect many (or any?) cell in order to avoid this situation where it is always trying to come back - and will do, when the immune system can't fight it off for some reason.
Please, if some specialist can analyze and comment on that it will be awesome.
More questions around it:
Is there the possibility that, while in this "dormant/attack" cycle, every single infected cell is defeated over the course of time, meaning an actual "cure"?
How does the cell replication process impacts the 1) hypothesis? (Maybe it is not possible for the immune system to achieve a natural cure because the virus keeps constantly replicating.)
How "much virus" would be needed for a successful strike in a compromised immune system (and how much compromised that system would have to be to fail)?
If the virus acts locally, is it possible for the vaccine to help other still-not-infected sites? In other words: is the natural immune response from the first infection in, say, the anus, worth anything for a subsequent infection in, for example, the oropharynx?