Thank you for joining the Intel communities.
I have tested this unit with wireless keyboard and mouse and I did not experience any problems.
You can see at the following link the wireless keyboard and mouse that Intel tested with this Intel® NUC.
To me this sounds a compatible issue because the old Logitech wireless combo works fine with your unit except for the Rapoo 8900p.
Do you have the latest BIOS version installed? If not, you could try a bios update; you can download the latest bios version here:
Please see F7 BIOS Update Instructions for Intel® NUC
Thank you for the information and I'm glad that this issue has been resolved, I hope you can have a better experience with the Intel unit from now on.