I found a solution to fix my own charger issue. The charger that came with the iPhone 4s was failing to charge the iPhone. But other charging methods were working. My iPad charger worked to charge my iPhone. A USB iPhone wire connected to my MacBook Pro also was able to charge the iPhone. But the low current, small wall wart consistently failed to light up a green charging image or bleep when plugged in.
The fix: Do a hard reset by holding the power button and the Home button until the iPhone does a hard reboot. After that, the small wall wart now works as I expect. There must be some intelligent power sensing logic in the iPhone that was out of calibration. I'm guessing that of all my power supplies, only the lowest current iPhone wall wart was below the mis-calibrated baseline current threshold. Resetting seems to have reset that minimum threshold.