Is there a condition where you can't grow toe-nails?

Many: There can potentially be many different causes. Since hair, skin and nails are all keratinized tissues there may be some relation. If your fingernails, toenails and hair all seem to grow slowly it is a sign of a potention nutritional deficiency or possibly some sort of environmental contaminant.

Not really: There is no specific syndrome where you can't grown toenails, but many things can affect toenail growth. Most common are fungus and trauma. See a podiatrist for an exam.

Onychomadesis: Is a condition where the nails shed off or fall off at there attachment by the cuticle region. It can be seen as a side effect of drugs, trauma, hand foot and mouth disease, illnesses with fevers, and poor nutrition.