Why was Harv sick in Diamond Age? Wouldn't they have technology to cure those kind of diseases? In other parts of the book, they used nanocytes as defenses to to 'cure broken capillaries in the buttocks'. Besides, he seems to come from hardy stock.
The sickness comes from all the nano tech in the air.
Part the First, Nell sees something peculiar; Harv explains all:
"See, there's mites around, all the time...They're in the air, in food and water, everywhere. And there's rules that these mites are supposed to follow, and those rules are called protocols. And there's a protocol from way back that says they're supposed to be good for your lungs. They're supposed to break down into safe pieces if you breathe one inside of you." Harv paused at this point, theatrically, to summon forth one more ebon loogie, which Nell guessed must be swimming with safe mite bits. "But there are people who break those rules sometimes. Who don't follow the protocols. And I guess if there's too many mites in the air all breaking down inside your lungs, millions– well maybe those safe pieces aren't so safe if there's millions."
As for why he wasn't cured, there's no specific cite but from the overall tone of the book Harv probably could have been cured if he was wealthy, powerful, connected, or "valuable". Since he's just a common street kid - tough luck.