  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 $8\times
10^{28}$s to $6\times 10^{28}$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 $8\times
10^{-13}$.
