2011 Chevy Aveo A/C - Strange Issue

Hello Aveo Experts...!

I have a 2011 Chevy Aveo that is currently having A/C problems. I've had the system checked for coolant leaks and low coolant but no issues. Compressor kicks on when pushing the green A/C button. Air continues to blow cool/regular air only. Here is the strange thing: While I was having my A/C system checked for leaks and low coolant the tech had the Aveo plugged into the computer. System error came up for bad battery (low voltage). I had the battery checked and sure enough, it was a bad battery. Tech told me that there is a chance the A/C was not pulling enough amperage from the battery and not kicking on correctly. I thought it sounded strange (doesn't a compressor get it's juice from the alternator??) but figured I would try the route of changing the battery before messing with the A/C compressor. Believe it or not, upon changing the battery the A/C began working! I could not believe it was blowing ice cold air again! Well my excitement was short lived because it stopped working again after going for a drive, turning car off and back on (~10 minutes later). I have no idea what could be going on... Is there a fuse or relay that could be bad? Why would replacing the battery solve my issue at first? Please help/let me know your thoughts...!

1) Compressors in most (this is changing because of the hybrids) cars are mechanically driven. What is electrical about a compressor is the clutch.
2) There are two kinds of electrical current needs initial and running. An electrical magnetic clutch can have a high initial current but a lower running current. The battery can supply a higher initial current.
3) I would check the ground going to the clutch or maybe a bad clutch