A supply chain is only as strong as its weakest link. Firms are constantly managing uncertainties, including unexpected delays in the provision of a critical input that can slow down or halt the production process, possibly making the manufacturer miss a delivery deadline. As most exporters are also importers of intermediate goods, supply chain unreliability related to import processing times at the border could impact downstream export dynamics. Exploiting a rich data set built on firm-level information for 48 developing countries over 2006-14, this paper relies on the Poisson pseudo-maximum likelihood estimator to investigate how unpredictability in border clearance times for imports affects manufacturing firms' entry, exit, and survival in export markets. The analysis finds that uncertainty in the time to clear imported inputs impacts neither the entry nor the exit rate, but translates into lower survival rates for new exporters, reducing the number of firms that continue to serve the foreign market beyond their first year of entry. This effect grows larger over time, owing to rising reputational costs to input-importing exporters, and is mainly driven by South-North trade, possibly reflecting the time-sensitivity of buyers in developed countries. The results also reveal heterogeneous effects across export industries, as well as the mediating role of sunk costs of entry in foreign markets, which attenuate the negative effect of uncertainty on survival rates, as firms delay exiting the export market. Most importantly, the measure of uncertainty displays a distinctive effect on export performance, as neither the mean nor the median time to import impacts survival.