>>12468105The immune system does respond (until it's too weak) but HIV evades it.
You do get HIV antibodies but antibodies only work on free/extracellular virus.
For viruses inside your cells the immune system uses the major histocompatibility complex to present virus fragments then killer T cells destroy infected cells. HIV interferes with the MHC/kT system so it can survive inside cells until the HIV antibody count outside goes back down, then it can get out and spread before antibody count goes back up.