We study the effect of imperfect sensing on the stability region of a cognitive radio system comprised of a set of source-destination pairs having different priorities. Interestingly, we found that even with non-zero sensing error rates, there exists a condition for which we can achieve identical stability region that is achieved with perfect sensing. This happens when relatively strong capture effect is present. For the case when the stability is sensitive to the sensing errors, we precisely quantify the loss due to the imperfect sensing in terms of the size of the stability region. Finally, we provide some general guidelines on controlling the operating point of the sensing device over its receiver operating characteristic.