This paper considers an iterative algorithm called the Interval-Passing Algorithm (IPA) which is used to reconstruct non-negative real signals using binary measurement matrices in compressed sensing (CS). The failures of the algorithm on stopping sets, also non-decodable configurations in iterative decoding of LDPC codes over the binary erasure channel (BEC), shows a connection between iterative reconstruction algorithm in CS and iterative decoding of LDPC codes over the BEC. In this paper, a stopping-set based approach is used to analyze the recovery of the IPA. We show that a smallest stopping set is not necessarily a smallest configuration on which the IPA fails and provide sufficient conditions under which the IPA recovers a sparse signal whose non-zero values lie on a subset of a stopping set. Reconstruction performance of the IPA using IEEE 802.16e LDPC measurement matrices are provided to show the effect of the stopping sets in the performance of the IPA.