Peer assessments, in which people review the works of peers and have their own works reviewed by peers, are useful for assessing homework, reviewing academic papers and so on. In conventional peer assessment systems, works are usually allocated to people before the assessment begins; therefore, if people drop out (abandoning reviews) during an assessment period, an imbalance occurs between the number of works a person reviews and that of peers who have reviewed the work. When the total imbalance increases, some people who diligently complete reviews may suffer from a lack of reviews and be discouraged to participate in future peer assessments. Therefore, in this study, we adopt a new adaptive allocation approach in which people are allocated review works only when requested and propose an algorithm for allocating works to people, which reduces the total imbalance. To show the effectiveness of the proposed algorithm, we provide an upper bound of the total imbalance that the proposed algorithm yields. In addition, we experimentally compare the proposed adaptive allocation to existing nonadaptive allocation methods.