I have a repair shop and every time i do a replacement i tell the customer it can be the battery or the software. In your case i would assume its the software. over time they can load up with info and apps and just drain even though the apps "appear" to be closed they are not. Do a software restore and delete any unwanted apps to see if this helps your problem.
do what Dak said. I had the exact problem and it seemed to be clear of any objects. I took it apart from the back and a few small parts from around my shop fell out of it. I thought i had to buy a new one and it started working perfectly. Be sure to pull the back off though and not just check the input where the paper goes.