There is growing evidence that brown dwarfs may be comparable to main-sequence stars in terms of their abundance. In this paper, we explore the prospects for the existence of life on Earth-like planets around brown dwarfs. We consider the following factors: (i) the duration planets can exist in the temporally shifting habitable zone, (ii) the minimum photon fluxes necessary for oxygenic photosynthesis, and (iii) the lower limits on the fluxes of ultraviolet radiation to drive prebiotic reactions ostensibly necessary for the origin of life. By taking these effects into consideration, we find that it is unlikely for brown dwarfs with masses 30M J to host habitable planets over geologically significant timescales. We also briefly discuss some of the major biosignatures that might arise on these planets, assess the likelihood of their detection, and highlight some avenues for further study.