I'm about to finish my first batch of Cornish X and have seen the same thing. The bird seems fine one day and then the next it just sits there. It will still eat, drink, poop, but won't move. Well maybe flap and scoot along.
I've posted about it as well and read as much as I could and the best I could come up with is that it's just something with the breed. I got my batch from Hoover's Hatchery. I only lost one chick out of 40, but I've had to process about 15 other birds early because of exactly what you describe.
I'd go ahead and process the bird. Get what you can out of it.
My next batch is going to come from Welp. They seem to specialize in the Cornish X and hopefully I won't have the problem.
Some things you should be sure you are doing:
1) They should only be fed twice per day. Take food away to prevent them from growing too fast, developing problems, etc.
2) Consider supplements. There are some that are specific to meat birds. Since they are fast growing the added nutrients can't hurt.
3) Have you tried Fermented Feed? There is a very very long thread on it. It is healthier for the birds and will cut down on your feed cost. Here is a shortened version of the thread:
http://tikktok.wordpress.com/2014/04/13/fermented-feed-faq/