It could be losing water when the system pressure is up. If you have an AutoZone part store near you, they will have a pressure tester you can rent at no cost (pay a deposit and you get it back upon return. Use the tester to put about 20psi in the system and check for any leaks. The tool will also have an adapter to test the radiator cap to make sure it holds pressure.
Tighten the clamps on the hoses, check the bottom of the water pump for any sign of a leak. There is a "weep hole" at the bottom of the pump for coolant to escape when the shaft seal goes bad. Also check where the pump bolts to the block. The gaskets can go bad and leak only when under pressure.
If you have the Z51 suspension package, check the hoses that run to the oil cooler. There is a metal pipe that runs from the cooler under the oil pan to a hose on the passenger side below and behind the A/C compressor. Lots of clamps on these lines so you may have to get the car up in the air to check them all.
If there is still no visible signs of leakage, you can have a "block test" run at a local auto repair shop. This test will find the presence of carbon monoxide in the coolant and can indicate a bad head gasket or crack in a cylinder head or block.