This is about a diesel Merc. I have driven it for about 4 years and the auto-stop feature has only worked (I think) twice, each time after a very long drive.
I presumed that this was because of standing idle every other day.
I’ve had a month off driving, with a small AA solar cell trickling a charge in. Today on returning to the car I got the warning message “please start engine, battery low”. I drove about 20 miles and the auto-stop started working. I wonder what’s going on. No thread drift please.
We had something similar with our F54 Mini. We bought it at one year old and stop/start feature worked regularly. After a few years it started to auto-inhibit with a corresponding brief message. Later still the AGM stop/start battery was replaced and after warming up it now regularly works again - rather annoyingly on most occasions! It can easily be overriden but resets on next startup

In your case it's highly likely the battery's capacity has diminished with normal ageing, to such a level that it can be re-charged to full remaining capacity quite quickly. The monitoring software see's a fully charged battery and allows stop/start function, whereas previously it would have required a longer journey. With such a limited capacity no amount of static charging will improve the situation significantly I'm afraid. The battery low message further confirms it's time for a new one.
After replacement It's very likely you will need to have the adaptive charge profile reset in the cars ECU to match as new. A message may appear asking for such, although car can be driven. Any garage should be able to perform this in a matter of seconds after plugging their tablet device into OBDII port and choosing your model.