After having fixed the battery and speaker issue, ( https://www.ifixit.com/Story/12618/iphon... ), I had noticed that even when plugged in, every now and then, the iphone 4S would just suddenly start discharging, as if it were not plugged in. Also, when I replaced the speaker in my previous repair, I did notice that there was some warpage of the old speaker assembly, as if that part of the speaker assembly got excessively hot. From those two things, I assumed there was a possible short in the dock connector assembly.
The repair went quite smoothly. That iScrews iPhone Screw tray comes in handy for the repair process, in making sure I know where every screw I removed went.
I delayed writing this success story, to verify that the intermittent discharging while plugged in problem was no longer present, and the problem is indeed fixed. Darned good thing I did buy the dock connector assembly even when I thought I didn't previously need it.
Replacing that rubber spacer can be rather tricky. Just take your time, and get a good light source.
iPhone 4S Dock Connector
iScrews iPhone Screw Trays
iPhone 4 and 4S Speaker Enclosure