Since early March we know, that there is the first patient which has been cured by HAART. According to the paper it has been proven that the infant was infected with HIV. This was done by detecting the virus even after the first 48 hours, this rules out that the virus transmitted by the mother without infection.
The infant was first treated when it was 30 hours of age with a triple therapy (zidovudin, lamivudin and nevirapin). On the seventh day the therapy was changed to zidovudin, lamivudin and lopinavir/ritonavir. After one month of therapy no replicable virus particle could be found. The therapy was continued until the age of 18 months. The infant is now 26 months without a sign of a rebound of the HIV infection.
The approach was atypical, since they used a therapy scheme with not established high dosing of the antiretroviral drugs. They ruled out a innate HIV-immunity by certain HLA variants, since Mother and child had matching HLA-Haplotypes. But other genetic mutations are still possbile.
This is scientific progress, the answer to your questions changes in only 2 months.