If your pit is too close to the surface, the ground could be frozen and not perc in winter. High water table also slows the perc rate. Then the pit stays filled up for a long time and the drains connected to it back up.
Is a larger pit feasible? Just so more water can be held and you can do more washloads in a row before the pit overflows. (You'll still have to wait until the water soaks into the ground.)
Don't let the weatherman string you along. Stick to your lawn watering schedule until it actually starts pouring.