I have a 2001, 2005 and 2010. The battery will go dead at 6-8 weeks idle due to computer and alarm draw. There are actually two solutions, which are the battery tender as mentioned which I use on two of my cars but the 2001 is in a car port with no power so I use a battery disconnect switch mounted in the battery area. Both solutions work well.

Do you have GPS in the car or nav system? If so make sure you  turn them off or unplug them. I have some  pictures of a burned up car because they left the GPS plugged in. You should unplug anything that you use, ie cell phone chargers. They have a constant draw on the battery.

I got a yellow top optumas &^ have not gone dead yet.... the delco was unpredictable

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I have a factory GPS, and haven't had any USB or anything plugged in all winter. I drove it last month, and it was fine. 

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My 2015 C6, Z51, had a dead battery.  I jump started it, and it started fine, but when I started to drive it forward, it would move, but the RPM stayed under 1400, in Drive.  I would shift to park, neutral or reverse, and it would Revline over 6000 RPM, and move in Reverse fast.  Just not in Drive or Low.......  Thanks to your help, I went and got a yellow top Optima battery, and like magic, it works fine.  Thanks to this forum and all you smart vette  guys.

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Looks like I'm odd man out here. I bought my 2012 GS last December. It had a 10 month old Optima yellow top battery. In January the car sat for five days and the car would not start. I took the battery to O'Reily's. They tested the battery and said it had a dead cell and because I did not buy the battery new it was not warrantied. I bought their store brand AGM battery. I have a Tender Jr pigtail wired into the Vette but don't normally hook it up because I drive it every few days. In April the car sat for 10 days without the tender and it was dead as a hammer. I charged it and then put the tender on it. The next day it was dead again. I charged it again and put the tender on it again. Since then it's been fine. I checked all the things mentioned here. Car was definitely off not in accessory, etc. Now I just make sure to start it every few days. I talked to my mechanic. He gave me a few pointers. He believes that when I charged the battery the first time it was charged enough to start the car but not fully charged. The tender was not enough to complete the charge and the battery died again. He said to always lock the car with the remote. He says even though you can't open the door without the fob the car is sitting there wait for a command. When you lock the doors it goes into a deeper "sleep" mode and turns off some of those things running in the background. I didn't intend to write a book but this is a consistent problem for a lot of people.