I'm gonna agree with Art on this one. My trailer started doing this as well. I think it comes from one brake wearing down more than the other (or not functioning at all). Once it wears far enough only one side engages and its at the very end of the actuator's stroke, which is why it locks and releases. It doesn't have any more pressure to hold the shoes to the drums.
When I went to adjust the brakes I noticed that one needed a lot more adjustment than the other. Getting them adjusted helped (for a little while), but one brake is definately working harder than the other, I just need to get the wheels/drums off to figure out which one and why.