Unstable network connections running on Docker (logged as interface renamed, device entered blocking/forwarding/disabled state or promiscuous mode)

Not really, unfortunately.

I suspect the problem being related to another problem which I keep experiencing and which I reported here Raspberry Pi 2 loses ethernet connection - #16 by Cplant and here Ethernet lost („eth0: carrier lost“) with NIC LEDs switched off - Raspberry Pi Forums.

In case you have any suggestion, let me know.