P.S.
Believe it or not the problem could be too much bathing.
A long time ago my older sister's daughter Maia was always sick too. Her doctor told my sister not to bath her everyday
just clean her up nightly before she went to bed.
Sponge baths were recomended.
She didn't give the child as many baths and wouldn't you know it, she stopped getting sick as often.
Now don't rule out what they say about building the ammune system with germs.