well, I charged the DSO while it was off: from the schematic in the manual it seems that the charging circuit is connected directly to the usb, before the on/off switch, so I thought it was the same (or better, it would charge faster without the power consumption of the instrument operation…)
anyway now the DSO is turning on correctly even after several hours of being off, so actually the problem is only the battery charge level, probably the first time I charged it (3-4 hours), the battery level after the charge was so low that it wouldn’t even turn on. after that i made a couple of cycles (charging several hours and discharging) and the things apparently got a little bit better
anyway, now even leaving the usb cable connected for a whole day, when I remove it in a few seconds the battery status goes again to low. I suppose that the problem is in the battery voltage readout. probably the charger reads a “full” value too early and stops charging.
Note: when the instrument turns off, I saw that the lcd backlight fades, so actually what causes the shutdown is really the battery going depleted, and not a wrong reading of the battery voltage (driving a software shutdown…)
I hope it helps… (and wait for a firmware upgrade!)