Hi, I'm Nathan.
Sorry to hear that you're having trouble with this but I'll do my best to help you, William.
This issue can be either handset itself, or the charger "base" or the power cord that supplies it.
The best way to test this is to see first if the handset will charge on the other base. If so, the handset itself is fine.
Next you'd swap the power plug "brick" (wall adapter) between the 2 charger stands, and observe if the handset will still charge on the larger "main" base while using the auxillary stations charger plug. If it does not, then the plug is bad. If it still does, then the charger stand itself is faulty.
Let me know the results, and I'll advise further on getting replacement parts (it can't be fixed, it would simply be replaced.