My PC keeps going into a weird "half-sleep" mode

I am struggling to articulate this properly, but my PC experiences a massive frame rate drop to about 5-10 FPS after three to five minutes of inactivity on the mouse or keyboard.
Essentially, when I am playing games that require mouse and keyboard input, everything functions normally; however, once I switch to sports titles using a controller, the frame rate collapses from a steady 60 down to a dismal 5 or 10. As soon as I touch the mouse again, the performance returns to normal.
The same issue occurs while watching movies or streaming content.
All power management settings and screensavers have been set to "never."
This issue began entirely out of nowhere about two or three months ago.
I have also ensured the power plan is set to maximum performance, so there are no energy-saving features active.
Why is this computer causing me such unnecessary stress?
Any assistance would be appreciated.

So, turns out that actually was the issue...

It still is.
I find it hard to believe that no one has come up with a solution yet; I've scoured countless international forums, and absolutely nobody has provided a remedy.