Recombination of free charge is a key process limiting the performance of solar cells. For low mobility materials, such as organic semiconductors, the kinetics of non-geminate recombination (NGR) is strongly linked to the motion of charges. As these materials possess significant disorder, thermalization of photogenerated carriers in the inhomogeneously broadened density of state distribution is an unavoidable process. Despite its general importance, knowledge about the kinetics of NGR in complete organic solar cells is rather limited. We employ time delayed collection field (TDCF) experiments to study the recombination of photogenerated charge in the high-performance polymer:fullerene blend PCDTBT:PCBM. NGR in the bulk of this amorphous blend is shown to be highly dispersive, with a continuous reduction of the recombination coefficient throughout the entire time scale, until all charge carriers have either been extracted or recombined. Rapid, contact-mediated recombination is identified as an additional loss channel, which, if not properly taken into account, would erroneously suggest a pronounced field dependence of charge generation. These findings are in stark contrast to the results of TDCF experiments on photovoltaic devices made from ordered blends, such as P3HT:PCBM, where non-dispersive recombination was proven to dominate the charge carrier dynamics under application relevant conditions.