Paging AggieAXO...
JMO, but I would tend to think it might be either of the aforementioned possibilities: health probs or depression.
One of my pugs is so close to me that whenever I have left in the past ten years, even to go to work, she has wailed for hours. Before I adopted my other dogs, she had to be taken to the pet sitter so she would not make herself sick from wailing. It has become MUCH better since we have adopted our other dogs!
She has a health problem that prevents her from being able to tell us she needs to go out to pee in time. So, we have to keep her on a VERY regular and frequent schedule (Usually, we take her out every two-three hours.) This has helped so much.
If it doesn't work to take the baby out more often (after giving it a chance to work), then I would take him to the vet to have everything checked out, including ruling out depression.