The Fermi Large Area Telescope (LAT) is detecting about 10% of the Fermi Gamma-ray Burst Monitor (GBM)-triggered GRBs that occur in its field-of-view. The spectra of the LAT-detected bursts show no evidence for cut-offs above the Band function EPeak in the 8 keV - 300 GeV energy range covered by the Fermi observatory. We present here an analysis of the 90% of GBM GRBs in the field-of-view of the LAT that were not detected. We obtain upper limits to the flux in the LAT energy range for the prompt emission of these GRBs and comment on the significances of these upper limits given the lower-energy spectral parameters of the bursts. Our aim is to establish whether the LAT is seeing all the GRBs one would expect given the characteristics of GRBs at lower energies, or whether there are any GRBs with evidence of spectral cut-offs.