I have owned a 2011 Terrain since Oct. 2014 and have not had any problems until March. Since then, I have had 2 batteries put in because if I don't use it every day, it will not start.
Sounds like you have a battery draw that exceeds the normal specs, as this is a 2011 the normal check out won't work as you need to isolate and preserve the systems presets, I would recommend taking it to a qualified shop so they can run the isolation test to fins what systems are staying active when they should be off, it could be the BCM not shutting down the accessories circuits.
I have a 2014 and twice I came out to a dead battery. Jump started, battery and the entire vehicle system checked out good both times. Still have the battery. It will be sitting for a month shortly, so we'll see what happens when I return home. If you changed batteries twice, like tennis shoes said, have the entire system checked. It will take several hours to run a full diagnostic on the entire electrical system.
Search GMC Terrain Questions
GMC Terrain Experts