We further develop an idea presented in a previous paper that the energy release process in solar flares can be understood as avalanches of many small reconnection events. We model the dynamics of the complex magnetized plasma of solar active regions with a simple driven dissipative system, consisting of a vector field with local instabilities that cause rapid diffusion of the field. We drive the system on a time scale much longer than the instability time scale and follow the evolution of the vector field and its statistical properties. Although energy is input to the system at a steady rate, it is released in discrete events, or avalanches. We argue that the avalanches in this model are analogous to solar flares