I was actually looking at this site because my baby just tested positive for celiac (blood). I stumbled upon the sleep sectioin, not realizing this was even a celiac symptom.
Over the past several years, I can count the times I slept through the night (6+ hours) on 1 hand. I wake up dozens and dozens of times each night, although I'm not sure why...was thinking my back/joint pain. It takes me hours and hours to fall asleep. My most restful time is probably from 4-6 am, although I'm still waking up, it's easier to fall back asleep. I have had back, neck and hip pain for years which has been attributed to car accidents from 20 years ago. I alternate between diahrrea and constipation, but rarely seem "normal." The fatigue is by far my worst symptom with the back pain being a close second. I can barely function every day. I feel like a zombie. I am bothered by loud stuff...tv, talking, toy noises, etc. I get migraine headaches (I think....I've never been diagnosed with them though). They come on sudenly and get so severe. Tylenol/Ibuprofen do nothing to help. The only way to get rid of them is laying down in a quiet, dark room and sometimes they go away by the next day...although I usually have a "sore" head for several more days. Ice on the back of my neck and forehead help a little during these episodes.
Are all these other things symptoms, too by any chance? Also, I was incredibly ill when I was pregnant with this baby (all my pregnancies were rough, requiring IV hydration due to hyperemesis), but this one was especially bad. I was in bed from very early on (before I even had confirmation I was pregnant) until the day I delivered and had a PICC line through the whole thing for fluids and Zofran. I had home healthcare nurses come about twice a week. Could the fact that he is celiac or maybe that I am celiac have anything to do with this? I've always had gluten in my diet and never even heard about celiac until just a few weeks ago.
The sleep problem may or may not be a symptom of celiac disease, but if your child has a positive diagnosis, you should definitely get tested yourself, as it is hereditary.

Luckily, my births have all been quick and not too problematic, 1 natural, the other 2 with epidurals (that only worked on 1 side), but all under 4 hours, the last one was only about 20 minutes of intense pain...I count my blessings on this as I've heard horror stories. Hope you continue to feel better!