Do you have picture/s?

Greg
Nevada

Three things come to mind - 1) root damage due to excessive watering which leads to #2 2) water less frequently but deeper. How deep is the water penetrating when you water, a couple of inches probably isn't enough (don't know your soil type, I'll guess a clay) 3) root damage from nematodes, can't think of any other critter that would damage roots.

A number of things can cause melon leaves to wilt, Ahips, Squash Bugs, Squash Vine Borer, Fusarium Wilt, Bacterial Wilt, or too much soil moisture as well as too little soil moisture.

I have had what Purdue calls "Sudden Wilt". They could not pin it down to any one thing. It appears to be a syndrone problem of perhaps a bit of fursarium wilt and other soil borne fungals. This sudden wilt will overnight wilt during the daytime and recover at night or on rainy days and after a couple weeks the plant is seriously hurt and in the meantime the plant cannot feed the nearly sized babies because of the stress to keep leaves hydrated. Classic fursarium wilt will strike in a more hit and miss pattern while sudden wilt hits the whole row [especially in lower and heavier soils] in unision.

Whatever the problem is, it's going to be too late to do something VERY soon. I would mound soil over every inch of stem as possible. Keep the soil moist but NOT soggy at all. Watermelons will put out new roots where a stem is slightly buried in moist soil. If your main roots are screwed, this remedy might allow the plant to set down alternate roots in time to save the plant. Good luck! :)

Here is a link that might be useful: Video demo of the procedure