D.B.
Could be a lingering virus, could be a second illness on top of an already compromised immune system from the first one. Could be aggravated by some allergies with post-nasal drip which can upset the stomach. Could be any of a number of immune system weaknesses (which most of us have unless we do something concrete to strengthen it) - most of these center in the digestive system.
Hydration is really important. Throwing up causes a loss of fluids of course, but low blood sugar from constant vomiting can itself cause nausea. Think of pregnant women with morning sickness - they get sick precisely because they have been sick. The balance of sugars and salt and water gets all messed up and the whole thing is just an ongoing cycle. Your son may be trapped in a similar "hamster wheel" of going nowhere.
I hydrate adults and kids with a highly absorbable drink (great for sports but great for everyone including kids and pregnant and nursing women) that gets into the cells and isn't just eliminated through urination. I use the regular drink but I also have people freeze it into popsicles which is a good way for sick kids and pregnant women to suck on it slowly but constantly. I also strengthen the immune systems. You could also try something available in the supermarkets although I find they aren't as reliable because they haven't gone through the testing required to get a patent.
Also, what's on the bland diet? There could be something in there that's throwing things off. Just because it seems bland and not spicy doesn't mean it's easy to digest. And if you're giving him anything that has emulsifiers in it (such as in many liquids to keep them from separating), that's a huge problem for a lot of people. That's one of the big problems with those heavily advertised protein shakes and drinks like Boost and Ensure - just a nightmare for most people to manage, especially those who are elderly or who have been sick.