Actually, the issue seems to be the player's inability to properly detect if it's online or not. For example, the player starts when no connection to a WLAN is established = it works only in offline mode. Connecting to a WLAN after the player was started does not help. The player reports to be in offline mode without any change (e.g. under the last.fm tab in regard to queued tracks submitting). I have to restart the player so it can actually detect a WLAN connection is on.

There is no problem with the player detecting offline state,though, so e.g. I switch the player on when a WLAN is connected -> the player correctly detects it's online -> the WLAN connection is dropped -> the player correctly detects it's now offline. In other words, it works one way, and doesn't work the other.