2004 Oldsmobile Alero A/C Core Leaking?

The A/C stopped working in my wife's Alero. No smells, visible leaks, etc - just no cool air coming out of the vents. I took it to a repair shop and they added refrigerant ($80). The A/C worked fine for about 2 1/2 months (but she doesn't drive the car very often), then no cool air again. Took it back to the shop, they replaced refrigerant again and added UV dye ($60). They reported no visible dye leak, said it probably indicated a bad core, but we should drive the car a couple of days, then bring it back for another look for a dye leak. We brought the car back 4 days later, again no visible dye leak. We were told this means a bad core, necessitating a $990 core replacement.

Before going ahead with this repair, I want to be sure that the diagnosis is correct. Does the absence of a dye leak truly pin down the problem to the core? Is there a more definitive test (sniffer?) That should be run before making this expensive repair? Is $990 a fair price for a core replacement?