The extent of immune restoration in HIV-1 patients on antiretroviral therapy is an important marker of disease progression. In this work, we investigate the dynamics of immune reconstitution and address the question of whether the early response to antiretroviral treatments allows to predict the late immune restoration. We select a cohort of twelve patients on GRT-HAART who achieve virological suppression, but show variable recovery of immune competence. HIV-RNA and CD4+ T cell assessments are used for estimation of the dynamic parameters of an established mathematical model of the viral-immune system interactions. We find that failure in immune reconstitution is associated with an abnormal increase of the death rate of uninfected CD4+ T cells. In contrast, their production rate is up to three times higher than in healthy seronegative individuals. This finding is in line with the view of chronic activation as a major cause of immune depletion. According to non parametric statistics, CD4+ T cell responders and non responders do not show significantly different dynamic parameters. Such result suggests that the employed model does not allow to predict the long term immune reconstitution.