So tonight a removed the battery and left it outside. In the morning I reinserted the battery, rebooted and the battery indicator had dropped from 7 hrs when idle to 5 hrs when idle. These numbers are not really consistent with the observations when the battery is in the device, but they indicate that the battery might discharge itself somewhat.
As a side note: with ASUI I did not manage to swich USB from HOST to OTG. It insisted on HOST. Does this ring any bells?