Efficient hyperpolarization of nuclear spins via optically active defect centers, such as the nitrogen vacancy (NV) center in diamond, has great potential for enhancing NMR-based quantum information processing and nanoscale magnetic resonance imaging. Recently, pulse-based protocols have been shown to efficiently transfer optically induced polarization of the electron defect spin to surrounding nuclear spins - at particular resonant pulse intervals. In this work, we investigate the performance of these protocols, both analytically and experimentally, with the electronic spin of a single NV defect. We find that whenever polarization resonances of nuclear spins are near degenerate with a "blocking"spin, which is single spin with stronger off-diagonal coupling to the electronic central spin, they are displaced out of the central resonant region - without, in general, significant weakening in the rate of polarization. We analyze the underlying physical mechanism and obtain a closed-form expression for the displacement. We propose that spin blocking represents a common but overlooked effect in hyperpolarization of nuclear spins and suggest solutions for improved protocol performance in the presence of (naturally occurring) blocking nuclear spins.@en