This is a known Gigabyte AHCI BIOS issue. BIOS update does not help, they never fixed the bug, at least it is not in the release logs. I updated the BIOS from F2 to F4 (not F5D, I don't want to have beta BIOS). The only difference I got is the infamous "23" message. (The registry tweak is a Windows issue, it has nothing to do with this bug, since this happens by drive recognition.)
It can be worked around this way by HDDs, but my DVD has the same issue, so it wont help. I'll stay with the IDE mode. It has slightly lower speed by the SSD, but that's irrelevant. TRIM works, that's what really matters.