After I had posted this troubleshooting walk-through, I had decided to just leave my Wii Remotes on the charger any time they are not in use. The reason for this was because the manual states that this system will NOT continue to try and charge the batteries once they are at 100%. (Makes sense of course)
Since I have started using it like this, I have had zero problems. I am wondering if these batteries are subject to the well known "rechargeable battery memory problem" that we all know and love. (For those who are unfamiliar, Google it!) At the same time, I am now wondering if the original cause of the issue is because sometimes only 1 of the batteries in the pack are charging. If so, it would make sense that the induction charger would not attempt to charge it any further because the battery pack is reporting that it is charged.
For anyone continuing to have problems with this system and who would like to do some troubleshooting on their own. I would like to challenge you to try something that came to mind while thinking about this problem.
1. Remove the battery pack from the Wii Remote that seems to have an issue.
2. Test the power/charge of each battery individually to see if one of them has a full charge, and if the other has no charge.
3. If only one of them has a charge, take note as to which one it is.
4. Locate a small light bulb or LED light. (Basically anything that can be powered by a single AA battery)
5. Connect the small light bulb or LED to the known working battery with two wires to see if it will light up.
6. If the light bulb turns on, leave it connected (tape it up if you have to) for a little while (5-10mins) to drain some of the power from the known working battery.
7. Remove the light bulb and wire setup after said time has passed and insert the battery pack back into a Wii remote.
8. Reset the induction charger by unplugging it from the wall, wait 10 seconds, then plug it back in.
9. Place the Wii remote back onto the induction charger to see if it charges longer than 5 minutes without the flashing red light.
10. Post on this blog whether it worked or not.
Final thoughts regarding this test:
By draining some of the power from the battery(s) by connecting a light bulb for a short while may reset the battery pack and allow the induction charger to reinitialize the charging process. I have ran into similar problems with rechargeable batteries that had not been fully discharged before charging them back up.
At the same time, if I experience the same flashing red lights as before, this process will be my next method of troubleshooting and I myself will post my results here as well.
I hope this works for someone and please keep me posted on your results.