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The quantum statistics of entangled photon pairs promise greater performance for absorption measurements than can be achieved classically. However, the performance of a quantum approach is easily degraded under a loss of photons caused by experimental limitations. Here, we propose a loss-tolerant quantum scheme using quantum destructive interference in a nonlinear interferometer. Our theoretical results show that the loss-tolerant quantum scheme surpasses the conventional quantum scheme under photon loss at the detection stage. We demonstrate how photon losses at optical paths and mode-mismatches in a nonlinear interferometer affect the performance of our scheme. We also propose a hybrid approach to cope with the case where the quantum destructive interference is imperfect, and show that the hybrid scheme always surpasses the conventional quantum scheme.