Crop rotation?

Those root maggots are the Cabbage Root Maggot and Ma, a fly like insect, lays eggs on the soil near the plants so when the eggs hatch the larva, the maggots, can find a food source, your radishes. Barriers on the soil that keep Ma from laying eggs can help, companion planting or intercropping can also help by confusing Ma so she isn't sure that a good food source is around. Floating row covers can keep Ma away, also.

The next time you plant radish seed do the following. It really works! Just before planting the seed fill the furrow with fresh, uncooked ground coffee . (I use the cheapest store coffee available.) Stir and combine with the soil slightly and plant the radish seed. Also a helpful treatment for any other root maggot problems.