A declining UV luminosity density at z>3 is found for dropout galaxies. Still a bit controversial, mostly due to big errors on the initial measurements at these high redshifts, but most people agree that it's real. Another interesting discovery is the luminosity-dependent evolution discovered in dropoout galaxies (cf. talks by R. Bouwens and I. Iwata).
An independent check: the accumulated stellar mass has to be produced. The found SFH's must be consistent with the assembled stellar mass. R.E. uses GOODs v-dropouts to estimate the stellar mass density at z~3-4. Part of the the sample have spectra, use these to calibrate the method (?, he went pretty quickly through those slides). They parametrize the SFH and compare with the found masses. The result is that there is too little SF going on to account for the stellar mass history. These stars could be formed in low-luminosity systems that occupy the faint end of the LF (and suffer from incompleteness).
A survey of lensed galaxies around a number of Abell cluster, have been able to deetct objects at very high z. Six objects have been found at z~10(!). The lensing is redshift dependent in the way that a specific region ("isophote") of the cluster is where objects of a certain redshift will fall. => bias against low-z galaxies. These galaxies might(?) have Lalpha emission, but is very faint in that case. They might contribute significantly to reionization.