Dynamic nuclear polarization (DNP) can increase nuclear magnetic resonance (NMR) signal strengths by factors of 100 or more at low temperatures. In magnetic resonance imaging (MRI), signal enhancements from DNP potentially lead to enhancements in image resolution. However, the paramagnetic dopants required for DNP also reduce nuclear spin relaxation times, producing signal losses that may cancel the signal enhancements from DNP. Here we investigate the dependence of H-1 NMR relaxation times, including T-1 rho and T-nu, under conditions of Lee-Goldburg H-1-H-1 decoupling and pulsed spin locking, on temperature and dopant concentration in frozen solutions that contain the trinitroxide compound DOTOPA. We find that relaxation times become longer at temperatures below 10 K, where DOTOPA electron spins become strongly polarized at equilibrium in a 9.39 T magnetic field. We show that the dependences of relaxation times on temperature and DOTOPA concentration can be reproduced qualitatively (although not quantitatively) by detailed simulations of magnetic field fluctuations due to flip-flop transitions in a system of dipole-coupled electron spin magnetic moments. These results have implications for ongoing attempts to reach submicron resolution in inductively detected MRI at very low temperatures.