One possible reason may be that your son is hungry for some reason, possibly because he is not getting enough calories on the special milk.he may be better on a soya milk.Do not be concerned about him not sleeping during the day all that much,but he should be sleeping better at night.Another possibility is that he may be having acid reflux when lying down. Give him Gaviscon Liquid 2.5ml at night and see if it relieves him so that he can sleep better.
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