Burning oil in 2004 Tahoe

In 2009, we discover the heads had a bad casting and porous cracks not visible to the eye, but failed a pressure test. So, they were replaced. Before the replacement, the vehicle did not burn oil. After, the vehicle is burning oil. I'm thinking it's the rings are failing, but it still gets good compression and no visible oil leaks are seen on the engine, or concrete drive. I'm not seeing a change in the coolant level and no overheating issues have been seen on this vehicle. What do you think it is and should I be concern a major breakdown is on the horizon? I'm having to place 1 quarter of oil every month. Example, oil change in Feb. 2011, End of March she was 2 quarters low.