Something similar happened to my 2009 Sedona. I bought it used from a GM Dealer Aug 2010 with 29,000 km on it.
It was an ex rental vehicle as well. It was in service for almost 9 months before it was purchased by a KIA dealer at an auto auction. The family that owned the KIA dealer also owned the GM dealership. With GM's restructuring, they decided to focus on GM only, and shut down the KIA 3 months later. All the remaining used vehicles were transferred to the GM lot next door.
Two months after I bought it, the battery started to fail on me. I went to the new KIA dealer (ex Mitsubishi) and they told me that there was a pro-rated warranty on the battery, with a direct replacement after a fixed period (which I was out of), then it pro-rates afterward.
They did cover half the cost of the battery.
A year later, my new battery started to fail as well, and they did replace the battery at no charge. They called my on my cell phone and told me the battery was in fact damaged. There was a dent in one side, and a bulge directly opposite. I did have rear end collision that was recently repaired at that point. The dealership told me they can warranty a defective battery, not a damaged one,and they wanted to put in a claim on it. I called my insurance company, who then honoured the battery claim as a follow up to the accident claim.
I have not had a problem with the battery since.