My iPhone 4S was preordered and received on the initial release date. The battery definitely was dying, and would stay charged less than a few hours. The battery capacity, according to the battery center tweak installed in ISX, was only 930 mAh.
I purchased a new OEM battery with tools for $9 on eBay, and found a YouTube video explaining the process.
It took me 10 minutes to replace the battery, and my iPhone is working like it did when it was new.
The hardest part was seeing the tiny screws to get them back into place.