Your ground looks dry, and melons don't much like transplanting at all.

Some of our starts did that too.They were either Squash or Watermelon and a Rhubarb.
A nursery person told me it may be that they need to harden off a little by bringing them outside and giving them partial sun/shade for awhile.
She said most windows now have UV treatments on them and the full sun may be too much for the little ones.
Another possibility is a late frost,which could have occurred to my plants. Brady

Melons seedlings have delicate roots and can be more difficult to transplant than other vegetables. Success requires either luck or experience combined with a light touch.

Did you pull the melon plants out of the peat pot, or did you plant the peat pot and the plant into the ground?

Your soil looks a bit cloddy and coarse for vegetable seedlings.

Did you have a cover crop? Looks like a lot of stray roots or something laying about, like the remains of a worked-in cover crop.

Edit: The gradual hardening off mentioned above can be important; how much time passed from indoors to in the ground for your plants?

This post was edited by larry_gene on Sun, May 26, 13 at 22:47

thanks for the feedback, it turned out they had root rot!!!