It's...profitable. But just barely. 25-30k cars a year from a factory that doesn't make anything else to offset the costs, and they have some pretty healthy costs in R&D...not a good formula for raking it in. Look at Corvette's longtime archrival, the 911. The Porsche starts at $90k, the Corvette is $55k. While I'm sure some P-Car fans would disagree, there isn't $35k more of car there. R&D and production costs are actually pretty similar between the two. But since the Porsche sells for so much more, it's a very profitable (one of the highest in all of the car biz) model.
Every so often, a movement gets started to try and branch Corvette off of Chevy as a standalone brand (like what was done with the Dodge Ram) to move the car upmarket and sell it out of Cadillac stores. But Chevrolet needs its halo car, so GM leaves it where it is and keeps it attainable to the middle class with a middle class price and a lot less profit in it.