I did some further investigation. Running
netstat -e 3
showed that every couple of seconds, the number of received packets in category dropped and error increased slightly.
Searching for DGS-1210 and 82579LM yields a D-Link document which states a known problem during auto negotiation with hardware revision B of DGS-1210 (mine is revision A) and that NIC, which can be solved by disabling power saving (i. e. EEE) on the switch.
So I disabled power saving on the switch and as a result, netstat stopped increasing the number of packets in category error and dropped. Finally, I've also disabled EEE on the NIC as suggested in the other thread (which on its own didn't solve the issue yesterday).
The system seems to have no frames dropped during the past 5 hours.