The so-called shock and kill therapies aim to combine HIV-1 reactivation by latency-reversing agents (LRA) with immune clearance to purge the HIV-1 reservoir. The clinical use of LRA has demonstrated detectable perturbations in the HIV-1 reservoir without measurable reductions to date. Consequently, fundamental questions concerning the limitations of the recognition and killing of LRA-reactivated cells by effector cells such as CD8+ T cells remain to be answered. Here, we developed a novel experimental framework where we combine the use of cytotoxic CD8+ T-cell lines and ex vivo CD8+ T cells from HIV-1-infected individuals with functional assays of LRA-inducible reactivation to delineate immune barriers to clear the reservoir. Our results demonstrate the potential for early recognition and killing of reactivated cells by CD8+ T cells. However, the potency of LRAs when crossing the barrier for antigen presentation in target cells, together with the lack of expression of inhibitory receptors in CD8+ T cells, are critical events to maximize the speed of recognition and the magnitude of the killing of LRA-inducible provirus. Taken together, our findings highlight direct limitations in LRA potency and CD8+ T cell functional status to succeed in the cure of HIV-1 infection.