Good estimates of HIV prevalence are important for policy makers in order to plan control programs and interventions. Although population-based surveys are now considered the "gold standard" to monitor the HIV epidemic, they are usually plagued by problems of nonignorable nonresponse. This paper uses the partial identification approach to assess the uncertainty caused by missing HIV status. We show how to exploit the availability of panel data and the absorbing nature of HIV infection to narrow the worst-case bounds without imposing assumptions on the missing-data mechanism. Applied to longitudinal data from rural Malawi, the Malawi Diffusion and Ideational Change Project (MDICP), our approach results in a reduction of the width of the worst-case bounds by about 18.2 percentage points in 2004, 13.2 percentage points in 2006, and 2.4 percentage points in 2008. We also use plausible instrumental variable and monotone instrumental variable restrictions to further narrow the bounds.