Re "If you are lucky you get one that works allright, if not, well, it was just bad luck." I think this must be the reason different owners are seeing such a range of battery life results from these very low priced radios; the supplied battery quality is highly variable.
I did just do an endurance check on my XHDATA sample:
Battery marking: 2000mAh
Test setup: adjusted volume to draw ~60mA (MW tuned between stations, i.e. white noise, enough volume to listen easily but not loud, backlight ON continuous which accounted for ~50% of current draw), battery fully charged (indicator shows 3 bars)
Ran until indicator showed one bar: 25.5 hours, i.e. 60 x 25.5 = at least 1530 mAh capacity demonstrated. I didn't want to fully discharge the cell so stopped there but volume and backlight brilliance had not noticeably changed so I'm sure there was some capacity left. Summary: I could listen for a full 24h day - with the light on - using the supplied cell.