This's a discussion for now, not really repairing technicality.

A cheap low quality, standalone ~4.4-4.5 V Li-ion battery charger for light torch is starting to get old. It's made for 2 loads in parallel.

In the past year it's been behaving weird, the polarity sometimes get reversed while every other thing is functioning normally perfect! So simply reverse the load, i.e. battery, polarity which simply works charging them till full. But on other time before being full while charging in reverse, it gets back to normal, i.e. original, polarity. So if not checked for too long beyond the usual full charge time limit, the charge result just getting back to reduce the battery voltages, and if caught so and the battery is reversed back to normal polar then the it'll get charged fully perfectly normal, the charger is not faulty, does not get reversed by its own for quite long time since then

So one expert or kind enough to shed lights on it for all of us?

 

"" A cheap low quality, standalone ~4.4-4.5 V Li-ion battery charger for light torch is starting to get old.
It's made for 2 loads in parallel. ""

First, Charging a Li-Ion-Cells with 4.5-Volts will definitely damage the Cells,
and possibly even start a Chemical-FIRE that You can't extinguish.
Therefore, Your Cells are already destroyed and dangerous.

The polarity-flipping is caused by the Cells being in a damaged state,
and probably because You have 2-Cells in parallel without proper Charging/Discharging Protection..

The best advice is to properly dispose of the Cells and the Flashlight,
and purchase a much higher quality Flashlight to replace it.

You have a poorly designed device that is not worth repairing, and is dangerous.

If You really want to abuse yourself, and custom build a top notch Flashlight,
You will find some ideas in the below Schematic ...........
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Tell us how you determined the polarity is reversed.