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A population experiencing habitat loss can avoid extinction by undergoing genetic adaptation—a process known as evolutionary rescue. Here we analytically approximate the probability of evolutionary rescue via a niche-constructing mutation that allows carriers to convert a novel, unfavorable reproductive habitat to a favorable state at a cost to their fecundity. We analyze competition between mutants and non-niche-constructing wild types, who ultimately require the constructed habitats to reproduce. We find that over-exploitation of the constructed habitats by wild types can generate damped oscillations in population size shortly after mutant invasion, thereby decreasing the probability of rescue. Such post-invasion extinction is less probable when construction is infrequent, habitat loss is common, the reproductive environment is large, or the population’s carrying capacity is small. Under these conditions, wild types are less likely to encounter the constructed habitats and, consequently, mutants are more likely to fix. These results suggest that, without a mechanism that deters wild type inheritance of the constructed habitats, a population undergoing rescue via niche construction may remain prone to short-timescale extinction despite successful mutant invasion.