A pic would help, but in general wilting is caused by not enough 'water pressure' inside the plant. If you have been watering them regularly it could be that the potting mix is holding too much water.

If so then the hair roots die and the plant becomes unable to take up the water even though the remaining roots are swimming in it.

I will leave it to you to determine if this is potentially the case. If so, stop watering and let the mix dry down.

Ah, sadly I don't have a digital camera. But they're not browning or yellowing, at least not initially, just wilting and not really growing at that point.

You could be right about the soil. I propped up the box a bit further up off the ground, and will take your advice about letting them dry out a little more before I water again.

Thanks!