Typically leaves dry up due to insufficient water, but you say they are well-watered, so a possibility is Alternaria leaf blight. From the photo it looks like a few leaves have yellow-brown spots. If at first the leaves had small, yellow-brown spots with a yellow or green halo on the oldest leaves, then the spots expanded and become large patches, then the leaves began to curl and die, it could be a fungal disease called Alternaria leaf blight. This disease will often occur when temperatures are high with lots of rainfall (which we had for a few weeks recently in our county). It is important to rotate your melon crops every two years to avoid disease problems.