hi Gayan,
I have used a number of these modules for many, many months, all OK.
The only problem was that the initial CR2032 cell that was supplied with the modules failed after after about a month, I guess it is the same as many manufacturers, they use cheap batteries in order to keep the costs down.
I have had no problems with the charging circuits, so far.
I suspect your problem is the inbuilt crystal oscillator, which is failing when the DS3231 gets 'hot'.
The ageing register programming just adds/subtracts very low value capacitors connected in parallel with main cap, which I understand is about 6pF.
The ageing register is normally trimmed/set by the manufacturer, you can add/subtract oscillator capacitance to adjust for a 'fast/slow' clock.
I do not set the ageing reg at power up.
Eric
Attached a copy of the DS3231 PDF.