We present and discuss the mean rest-frame ultraviolet spectrum for a sample of 81 Lyman Break Galaxies (LBGs) selected to be B-band dropouts with a mean redshift of z=3.9 and apparent magnitudes z_AB<26. Most of the individual spectra are drawn from our ongoing survey in the GOODS fields with the Keck DEIMOS spectrograph, and we have augmented our sample with published data taken with FORS2 on the VLT. In general we find similar trends in the spectral diagnostics to those found in the earlier, more extensive survey of LBGs at z=3 undertaken by Shapley et al (2003). Specifically, we find low-ionization absorption lines which trace the presence of neutral outflowing gas are weaker in galaxies with stronger Lyman-alpha emission, bluer UV spectral slopes, lower stellar masses, lower UV luminosities and smaller half-light radii. This is consistent with a physical picture whereby star formation drives outflows of neutral gas which scatters Lyman-alpha and gives rise to strong low-ionization absorption lines, while increasing the stellar mass, size, metallicity, and dust content of galaxies. Typical galaxies are thus expected to have stronger Lyman-alpha emission and weaker low-ionization absorption at earlier times (higher redshifts). Indeed, our mean spectrum at z=4 shows somewhat weaker low-ionization absorption lines than at z=3 and available data at higher redshift indicates a rapid decrease in low-ionization absorption strength with redshift. We argue that the reduced low-ionization absorption is likely caused by a decrease in the covering fraction and/or velocity range of outflowing neutral gas at earlier epochs. Our continuing survey will enable us to extend these diagnostics more reliably to higher redshift and determine the implications for the escape fraction of ionizing photons which governs the role of early galaxies in cosmic reionization. [Abridged]