Is it rare for the body not to fight off hpv and warts never go away on their own? is it common for them to last more than 2 years?

Different from flus or other systemic viruses that enter your blood, HPV strains are surface dwellers. They enter and grow in superficial skin layers with minimal exposure to the bodies immune surveillance system. Most clear in 2 years. I am aware of people who have had HPV wart strains that persisted for decades. You can have them frozen/acid killed or lasered off.