To date no direct detection of Lyman continuum emission has been measured for intermediate–redshift ( z \sim 1 ) star–forming galaxies . We combine HST grism spectroscopy with GALEX UV and ground–based optical imaging to extend the search for escaping Lyman continuum to a large ( \sim 600 ) sample of z \sim 1 low–mass ( \mbox { log ( $ \overline { \mbox { M } } $ ) } \simeq 9.3M _ { \odot } ) , moderately star–forming ( \overline { \Psi } \lesssim 10 M _ { \odot } yr ^ { -1 } ) galaxies selected initially on H \alpha emission . The characteristic escape fraction of LyC from SFGs that populate this parameter space remains weakly constrained by previous surveys , but these faint ( sub– L _ { \star } ) SFGs are assumed to play a significant role in the reionization of neutral hydrogen in the intergalactic medium ( IGM ) at high redshift z > 6 . We do not make an unambiguous detection of escaping LyC radiation from this z \sim 1 sample , individual non–detections to constrain the absolute Lyman continuum escape fraction , f _ { esc } < 2.1 \% ( 3 \sigma ) . We measure an upper limit of f _ { esc } < 9.6 \% from a sample of SFGs selected on high H \alpha equivalent width ( EW > 200 \mbox { \AA } ) , which are thought to be close analogs of high redshift sources of reionization . For reference , we also present an emissivity–weighted escape fraction which is useful for measuring the general contribution SFGs to the ionizing UV background . In the discussion , we consider the implications of these intermediate redshift constraints for the reionization of hydrogen in the intergalactic medium at high ( z > 6 ) redshift . If we assume our z \sim 1 SFGs , for which we measure this emissivity-weighted f _ { esc } , Â are analogs to the high redshift sources of reionization , we find it is difficult to reconcile reionization by faint ( M _ { UV } \lesssim - 13 ) SFGs with a low escape fraction ( f _ { esc } < 3 \% ) , with constraints from independent high redshift observations . If f _ { esc } Â evolves with redshift , reionization by SFGs may be consistent with observations from Planck .