My wireless keyboard does not work properly on my Fedora 32 desktop. Specifically, when I leave the keyboard unused for about 20 seconds, it will not respond when I resume using it.
Actually, I had this issue since Fedora 31 for my desktop. However, my Fedora 32 laptop does not have this issue. I suspect that this may be a hardware issue, but I still want to see if anyone has encountered and solved this issue.
I have a wireless keyboard too and I experience similar issues.
It could be that your keyboard gets unloaded after a period of inactivity. Probably it takes X time to detect and load your keyboard again.
To find out you might want to examine your boot log and filter it with this command: sudo journalctl -b _COMM=gdm-x-session
I have used logitec wireless keyboards and mice (using the logitec unfied receiver) for many years and have never seen the problem you list here.
I have never had to do any config within fedora since that receiver works at the bios level with almost all hardware.
The only times I seem to have any difficulty is when the battery in the keyboard or mouse gets weak, then I simply replace the battery and everything is fine again.