Answer: Maybe you have been too "nice" to them! Usually it is one of two things: either there is too much nitrogen or you have planted them too late. They are not terrribly heavy feeders so a well-worked and deep, well-drained yet moist soil with a pH between 6 and 8 should be sufficient. Radishes can be planted quite early and really grow best when temperatures are very cool, ranging from 60 to 65 degrees. Since it sounds like you have spent some effort on your garden soil, you might be able to cut back on some of the fertilizing when it comes to radishes.
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