Determined by the many factors. Infection by another DNA strain (being infected by one strain does not mean you are safe from others) and health of immune system are two contributing factors to keeping active infections at bay.
HPV is not like HSV. HSV has periodic outbreaks that are caused by the virus. HPV does not have this. Depending on which type (high risk or low risk) of HPV one has, one may not have any outbreaks (warts) at all.