(Abridged) By means of high-resolution cosmological simulations in the context of the LCDM scenario, the specific star formation rate (SSFR=SFR/Ms, Ms is the stellar mass)--Ms and stellar mass fraction (Fs=Ms/Mh, Mh is the halo mass)--Ms relations of low-mass galaxies (2.5< Mh/10^10 Msun <50 at redshift z=0) at different epochs are predicted. The Hydrodynamics ART code was used and some variations of the sub-grid parameters were explored. Most of simulated galaxies, specially those with the highest resolutions, have significant disk components and their structural and dynamical properties are in reasonable agreement with observations of sub-M* field galaxies. However, the SSFRs are 5-10 times smaller than the averages of several (compiled and homogenized here) observational determinations for field blue/star-forming galaxies at z<0.3 (at low masses, most of observed field galaxies are actually blue/star-forming). This inconsistency seems to remain even at z~1.5 though less drastic. The Fs of simulated galaxies increases with Mh as semi-empirical inferences show, but in absolute values the former are ~5-10 times larger than the latter at z=0; this difference increases probably to larger factors at z~1-1.5. The inconsistencies reported here imply that simulated low-mass galaxies (0.2<Ms/10^9 Msun <30 at z=0) assembled their stellar masses much earlier than observations suggest. This confirms the predictions previously found by means of LCDM-based models of disk galaxy formation and evolution for isolated low-mass galaxies (Firmani & Avila-Reese 2010), and highlight that our implementation of astrophysics into simulations and models are still lacking vital ingredients.Comment: 17 pages, 7 figures. ApJ, accepted. Minor changes after Referee's report. Some new references adde
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