Why does my Realtek gigabit NIC not advertise 1000Mbit mode?

I currently have a NAS (openmediavault based on debian) with a Realtek gigabit NIC (ASRock Q1900-ITX on-board LAN), but it won't advertise that it is gigabit-capable. ethtool eth0 gives the following output:

Settings for eth0:
    Supported ports: [ TP MII ]
    Supported link modes:   10baseT/Half 10baseT/Full 
                            100baseT/Half 100baseT/Full 
                            1000baseT/Half 1000baseT/Full 
    Supported pause frame use: No
    Supports auto-negotiation: Yes
    Advertised link modes:  10baseT/Half 10baseT/Full 
                            100baseT/Half 100baseT/Full 
    Advertised pause frame use: Symmetric Receive-only
    Advertised auto-negotiation: Yes
    Link partner advertised link modes:  10baseT/Half 10baseT/Full 
                                         100baseT/Half 100baseT/Full 
                                         1000baseT/Half 1000baseT/Full 
    Link partner advertised pause frame use: Symmetric Receive-only
    Link partner advertised auto-negotiation: Yes
    Speed: 100Mb/s
    Duplex: Full
    Port: MII
    PHYAD: 0
    Transceiver: internal
    Auto-negotiation: on
    Supports Wake-on: pumbg
    Wake-on: g
    Current message level: 0x00000033 (51)
                   drv probe ifdown ifup
    Link detected: yes

1000Mbit full duplex is supported by the driver and the board (as stated in hardware specs). The connected switch does advertise that mode, however the NIC does not.

Attempting to change the advertised mode with ethtool -s eth0 advertise 0x020 or at least forcing the NIC into gigabit mode does not help. The command returns without any error message and the NIC goes down. After bringing it back up with ifup eth0, speed and advertised modes are still set as they were before the change. The cable is cat6 and changing the cable does not solve the issue.

How can I get that network interface to advertise gigabit speed?