Sorry to resurrect this topic but i had the same issues when back then i updated my BIOS from an ASUS Z170 PRO GAMING mobo to the latest version last year on November around..Logitech G510 too!!!
The thing is that ASUS has now released a BIOS update for my board... There's ofcourse newer versions above the one i'm going to say, but this one, the BIOS 3402 says the following (Note: From 19/05/2017)
Versión 3402 2017/05/197.74 MBytes
Z170 PRO GAMING BIOS 3402
1. Fix keyboard can not enter into BIOS issue. (SteelSeries)
2. Fix M.2 NVMe SSD issue (Plextor)
....Yes, SteelSeries, but maybe it helps with all Logitech KBs?... The actual version is 3610 wich just improves memory stuff..
I won't update my Z170 PRO GAMING unless someone with the same board and Keyboard (Though now i use a Logitech G213) can dare to update their BIOS to the newest version (3610) and even record it working out... (Aka Access BIOS with newest update, with the keyboard, and in the same process show off the BIOS version...)