2 catalytic converters

My niece has a 2000 infiniti I30. she bought in 2004, this year(09), the svc lite comes on, she takes it to the dealer who runs a diagnostic, says the catalyic coverter(?bay 1) is bad (states it has 2).

replaces the cat. resets the svc lite and she is driving home and the lite comes on again. She turns around, they run another diagnostic and tells her the other is bad and needs to be replaced. She has to go to DEQ (inspection) that day. She gets them to shut off the svc lite, they tell her to drive there, Do Not turn of the car, she does that, they do the DEQ diagnostic and it passes with flying colors. She goes home,turns off the car and turns it back on and the svc lite is indeed on again!.

Could the DEQ diagnostic not pick up on a bad catalytic coverter even if it does have 2…and does it have 2?

Those error codes do not directly indicate that a specific part is bad.
They only say a sub-system isn’t working right.
Maybe 75% of the cars that give that code have a bad converter, and you’re one of the 25% with something else.
Even at dealerships there are workers who change parts first and ask questions (troubleshoot) later.

Post here and tell us the code numbers. They look like P0123.