We follow the bright, highly energetic afterglow of Swift-discovered GRB 080721 at z = 2.591 out to 36 d or 3 x 106 s since the trigger in the optical and X-ray bands. We do not detect a break in the late-time light curve inferring a limit on the opening angle of and setting tight constraints on the total energy budget of the burst of E luminance greater than or equal to 9.9 x 1051 erg within the fireball model. To obey the fireball model closure relations, the gamma-ray burst (GRB) jet must be expanding into a homogeneous surrounding medium and likely lies behind a significant column of dust. The energy constraint we derive can be used as an observational input for models of the progenitors of long GRBs: we discuss how such high collimation-corrected energies could be accommodated with certain parameters of the standard massive star core-collapse models. We can, however, most probably rule out a magnetar progenitor for this GRB which would require 100 per cent efficiency to reach the observed total energy.