Once a wk it wont start for a day or two

Are there any warning lights on? Security light?

I have exactly the same problem only it does it every morning when i wake up. I have to re-teach the ignition for 30 minutes every morning to get my car to start. I have exactly the same make, year and model as you. I have been asking around for a few weeks now and it seems to be a problem with the ignition lock cylinder. this is typically around a $300 to $400 dollar repair however i am going to get quotes on the repair tomorrow. There is a pass lock senson enbedded within the ignition cylinder from what i understand and apparently this is what is bad.

I have an 04 CTS and it does the exact same thing. I work offshore for 28 days at a time, if my girl doesn't drive my car while I'm gone it'll do exactly what your talking about for a few days. I disconnect the battery and as I'm screwing the post back in it'll make a clicking sound. Once I hear that sound I get in and crank it up then finish tightening the side post. I've asked about this for a long time but no one knows anything about it. If you find anything out please let me know!