We report on constraints on the lifetime of decaying gravitino dark matter in models with bilinear R-parity violation derived from observations of cosmic-ray antiprotons with the PAMELA experiment. Performing a scan over a viable set of cosmic-ray propagation parameters we find lower limits ranging from $8times 10^{28}$s to $6times 10^{28}$s for gravitino masses from roughly 100 GeV to 10 TeV. Comparing these limits to constraints derived from gamma-ray and neutrino observations we conclude that the presented antiproton limits are currently the strongest and most robust limits on the gravitino lifetime in the considered mass range. These constraints correspond to upper limits on the size of the bilinear R-parity breaking parameter in the range of $10^{-8}$ to $8times 10^{-13}$.
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