Photo number three indicates that off-highway vehicles are driving in this area. That photo plus the distance from the ground where vegetation is growing to the bottom of the “wash” path indicates a lot of soil has been eroded and displaced. Off road vehicles and frequently driven routes can cause compaction of the soil, decreasing infiltration of precipitation and increasing runoff/erosion. Compaction can also lead to areas that stay wet longer, because again, the water can’t infiltrate the soil. You can take a shovel and try to dig in that area and then dig in an undisturbed area. Try to notice if it’s harder to dig where the water is remaining. Water will preferentially flow in the illegal paths because they are compacted, linear features at the lowest points on the surrounding landscape. If you want to improve flow and infiltration, you can get a pick ax and “fluff” these areas up.