HIV-associated neurocognitive disorder is known to occur in the context of successful combination antiretroviral therapy (cART; plasma HIV RNA <50 copies/ml). Here, we newly provide an analysis of its prevalence and nature in the absence of medical or psychiatric confounds that may otherwise inflate the prevalence rate. We enrolled a cohort of 116 advanced HIV + individuals on cART (51% virally suppressed (VS)). They were screened for active Hepatitis C, current substance use disorder and were assessed with standard neuropsychological (NP) testing. Our results showed that out of the entire sample, NP impairment occurred in 18.1% (21/116) in VS individuals which was not statistically different from the 24.1% (28/116) that were found to be NP-impaired and not VS. In comparison with NP-normal-VS persons, NP impairment in VS individuals was associated with shorter duration of current cART and lower pre-morbid ability. Higher cART CNS penetration effectiveness tended to be associated with lesser cognitive severity in NP-impaired VS individuals. Current CD4 cell count, depression symptoms and past CNS HIV-related diseases did not specifically account for persistent NP impairment in VS individuals. In conclusion, despite suppression of systemic viral load, non-confounded HIV-related NP-impairment prevalence reached 18.1%. Of the potential explanations for this persistent deficit, a “burnt-out” form of the disease and immune reconstitution inflammatory syndrome were the less likely explanations, while a shorter current cART duration and lower pre-morbid intellectual capacity were significant. Nonetheless, predictive modelling with these last two factors misclassified 27% and had low sensitivity (43%) emphasising that other yet-to-be-defined factors were operative.