In this paper we investigate the design of a low-delay robust streaming PIR scheme on coded data that is resilient to unresponsive or slow servers and can privately retrieve streaming data in a sequential fashion subject to a fixed decoding delay. We present a scheme based on convolutional codes and the star product and assume no collusion between servers. In particular we propose the use of convolutional codes that have the maximum distance increase, called Maximum Distance Profile (MDP). We show that the proposed scheme can deal with many different erasure patterns.