We haven’t even managed to wipe out polio, and that is a cheap, lifelong vaccine.
If new generations are not also given the vaccine, it will eventually return.
Probably the same with HIV, although I could see it being somewhat more difficult for that to make a resurgence. If we inoculated the entire human race against it, it could possibly eradicate HIV for several generations, if not permanently.
Either they evolved from a different human virus, or from an animal virus.
Measles for example evolved from a livestock virus called rinderpest and lost the ability to infect cattle as it became a specialized human virus.