Next 20 years? No chance. The virus is near perfection from a genetic point of view as it has genes across all three reading frames, something that was thought to be impossible before HIV was discovered and its genetic material was unraveled. You also don't have 1 single type of HIV in your body if you are infected, as they mutate so quickly, they render medical treatments useless. The retrovirals we invented now also have a poor prognostic result, as HIV can also go dormant whilst the viral load is lowered by medication to then resurface again as a completely different phenotype via mutation.
We'll cure most cancers before we stop HIV.