Although population-based surveys are now considered the "gold standard" for estimating HIV prevalence, they are usually plagued by problems of nonignorable non- response. This paper uses the partial identification approach to assess the uncertainty caused by missing HIV status due to unit and item nonresponse. 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, our approach results in a substantial reduction of the width of the worst-case bounds. We also use plausible instrumental variable and monotone instrumental variable restrictions to further narrow the bounds.