In ground insects are hard to kill off. The issue may be cutworm or other kind of worm - (Earth worms are good).
Last year I let my vegetable garden lay fallow (un-planted) I weeded it, removed all the mulch, turned the soil,and watered it. Then I covered it in clear plastic holding down the sides with wood covering the whole bed.
That summer the sun cooked the soil, Once a month I would go out, uncover it and turn the soil again, level, watered and covered with plastic. It was the same summer when I expanded and raised the beds with redwood, leveled and planted grass in the middle. I took that year off from vegetable growing to let the soil rest. There is a good reason why God told the Jews to plant and harvest for six years and do not planting the seventh.
Soil is much more than just a good place to put down roots. It supplies food and water for plants. Good soil is something that is built up. Most of the vegetables we plant are rough on the soil and strip out the nutrients. Once that happens the plants become weaker and this allows pests and disease to take hold.
Insects in the soil will soon take over. Once they get started you either have to use poison or you have to take away the food supply so their population dies off. Diseases can stay in the soil for years- Certain fungus and molds never leave but can take over rapidly if the health of your plants is compromised due to poor quality soil.
I have been building up the soil in my garden for the past 8 years. I use lots of mulch (Grass trimmings, leaves, hay, shredded paper shredded bark, coco beans husks (We have a Hershey plant near by) and other things. I also have a few compost bins where most of my yard waste and food wastes (not meat) go. I use succession, intensive and companion planting methods, plus I exercise a good deal of planning years in advance. I keep past maps of my garden so I know what I planted where last year so I do not repeat in the same place.
Last fall when it came time to plant my late crop I found I had far less trouble with pests in the soil. The clear plastic baked the soil. It would let the heat and light in making a hot house effect under the plastic. By turning the soil I brought the deep things up near the top to be cooked. I starved the bugs too by not giving them anything to eat. I made their neighborhood a bit of a hell. They moved out (or died)
You must rotate your crops year to year. Things like potatoes can not be followed with tomatoes, I would suggest looking up crop rotation, succession planting and companion planting at your local library. These are intensive and Organic Gardening Techniques which work rather well. There are many books on the subject - Use the Library, read the books and when you find a good book that you like then purchase it.If you just run out and buy any old organic gardening book you may find it sits on the shelf and you are buying more than you need.
Tomatoes need to make the rounds at least 3 years without being planted in the same spot due to the kinds of insects that live in the ground. Other things like potatoes will get diseases which will infect the soil and attack the roots of other plants. some plants, like marigolds, are helping plants a companion plant which acts as a defense against pests. Garlic and Onions also act in this manner - but be careful, potatoes don't like Garlic and Onions.
Other than poison there is nothing you can do this year to save your radishes.
Less watering may help. I know that sounds like a contradiction, however radishes will spit if they grow to fast, this makes for an easy in for the pests. Other root crops can grow to fast as well, carrots, turnips, parsnips, etc. Less watering tends to slow down the growth which keeps splitting from taking place as often.
Radishes are a Cool Weather Crop - Meaning they prefer the soil to be colder than the summer baked soil that Corn, tomatoes and Pole Beans love. You can lower the temperature of the soil by laying aluminum foil between your rows until the radish tops shadow the soil. Early Spring and mid to late fall are good for things like carrots, radishes, turnips, lettuce. Mid summer is good for Tomatoes, Beans, Corn, watermelon.
Knowing your zone (5 is it?
) and knowing the temperature of the air and soil may go a long way in selecting the right crop for the right time. Succession Planting is a subject that goes in depth on this and can also give you good hints on how to extend the growing season of different plants, and also will tell you what kind of vegetables do well following the last crop.
EXAMPLE: Lettuce, spinach and other leafy vegetables are good to plant in the place where you will be starting you corn. As you are nearing the end of the Leafy Green Season you should have already started the rows of Corn and they should be nearly tall enough to dwarf the greens. Corn requires a certain set of nutrients that leafy greens don't need, while the leafy greens have already stripped certain nutrients from the soil that corn can go without. The following year you would plant something like beans in the same place since the corn husks and stalks are now rotting in that area and slowing releasing nitrogen into the soil which beans like.
It is the circle of life micro-organized by you.
companion planting (which that link above talks about) is an excellent way to protect plants from pests. It is not 100%, it is a 80% proposition. Organic Gardening is organic, so expect to get 1/2 to 2/3 of your crop and Nature taking her share. If you get better than that, good. But don't expect to be getting 100% of your crop.
Maybe something out of this long answer may help you.
Cheers
Thanks TREE. I already checked out most of the sites about radishes, what I was looking for was some up front personal experiences. I've been gardening for about 40 years, and have always had a problem with the insects sharing my crop. I don't like using Diazanon & some of the other chemicals, and wondered if someone had some other ideas. 
