Another photo

photo of leaf

In Hot summer days, when that plants are established, and fruiting, the lower leave that mostly are shaded will fade away. BUT in your case it seems to be different, AS IF the leaf in the picture is chewed by some critter.
PS
A picture of the whole plant could be more helpful.

That looks an awful lot like Squash Vine Borer frass to me.

If you had SVBs in the main stem, the whole plant would be suffering, but since you say it's only the lower leaves, probably something else.

I wish it was something else. I looked up some pics about SVB and I think that's what it is. Here's a pic of the whole plant. Looks beautiful! but the lower leaves are yellowing/browning. It's probably just a matter of time before the whole plant croaks

A pic of the stem

Perform surgery and cut out the borer. Then bury the stem along the vine both at the damaged part and other places. It should form new roots. You can probably save your plant.

Yes, make sure you inspect the vine for additional eggs, and then once clear, bury as much of the vine as possible. It will develop more roots. I've gotten pumpkins from vines damaged from SVB, in part because they don't always completely sever the vine, and also because of the extra rooting that occurs along the vine.

This post was edited by ccabal on Wed, Jul 24, 13 at 12:33

Also regarding surgery... a less invasive method is to try and find the entry point, or the hole where the frass is coming out from. Then wash it out, and get a spray bottle, set to stream mode. And spray into the hole some soapy water. Spray it pretty good. Often the grub will come out of the hole to try and escape the water, and you can kill it, or the soapy water might kill it. I also will poke a wire into the hole to stab it or fish it out. Either way this might be less damaging to the plant than having to split it open.