Human body does not kill HPV virus on its own and treatment has to be planned to remove them. Treatment options include several medications(like podophyllum resin, Podofilox (Condylox), Trichloroacetic and bichloroacetic acids, Imiquimod 5% cream and interferons) are available, which can be applied directly to the surface of the warts. Other treatment options include electrical cautery, surgical removal, Carbon dioxide laser treatment and electrodesiccation.
Since the wart is recurring, so you can resort to laser treatment also.
I hope it helps. Take care and regards.
I also had a common wart on my thumb for about 4 years...that is, until I clipped it off with fingernail clippers (I cut deep enough to make it bleed) and then applied generic super-glue to the site, re-applying it everyday to ensure a good seal. I know super-glue has arsenic in it, but from what I understand it will only hurt you if you apply it to a really deep wound where the arsenic can get into your blood stream in appreciable amounts.
This may or may not work for you, but if you're really bothered by the wart it probably wouldn't hurt to try.