HIV becomes AIDS when the body does not have the necessary defense to fight regular infections (See @Kusadikika above). HIV does not necessary kill you; what kills you are the TB, pneumonia, meningitis, diarrhoea and fungal infections, which the body cannot fight any more.
HIV is virus, that mutates too fast for stem cell therapy to have any significant effect. Stem cell therapy works well for leukemia, since it is not an infection, and the cancer cells are well replaced by the more rapidly dividing stem cells. Stem cell therapy is, however, socially, ethically and medically controversial.
IMHO, if HIV/AIDS was a greater caucasian problem like ahlzeimer and cancer are, there would be more extensive research and probably a cure by now. But it will remain a problem of sub-Saharan Africa.
Set out to correct the world's wrongs and you will most certainly wind up adding to them.