  It has been suggested that cosmological gamma-ray bursts (GRBs) can produce
the observed flux of cosmic rays at the highest energies. However, recent
studies of GRBs indicate that their redshift distribution likely follows that
of the average star formation rate and that GRBs were more numerous at high
redshifts. As a consequence, we show that photomeson production energy losses
suffered by ultrahigh energy cosmic rays coming from GRBs would produce too
sharp a spectral high energy cutoff to be consistent with the air shower data.
Furthermore, we show that cosmological GRBs fail to supply the energy input
required to account for the cosmic ray flux above 10 EeV by a factor of
100-1000.
