On a 3080 FTW3, I have two monitors: a Displayport connected monitor (primary) + an HDMI connected monitor (secondary; my audio goes out via HDMI to a receiver). When I come back to my computer after a while (both monitors off) and turn on my primary DisplayPort-connected monitor, the LED shows that it's in standby, however, moving my mouse and typing on the keyboard doesn't wake the monitor out of standby.
 
I assumed my machine had BSODed and was about to hard power-off until saw that the HD activity light still going. So I powered on my secondary HDMI monitor and suddenly both monitors displays come up.
 
I've done some tests, and find that if I use either my mouse or keyboard before the monitor has fully powered on -- which I typically do simultaneously as I power on my monitors to wake the wireless mouse/keyboard to then wake the displays -- the monitor never gets pulled out of standby mode. If I wait until the monitor fully powers on and then enters into standby mode, and then I use mouse/keyboard, the monitor gets the signal to wake up.
 
So it seems there's a driver bug which isn't properly detecting a standby'ed monitor and/or passing along a wake event to the monitor via Displayport. If I use any mouse/keyboard input before the monitor is fully powered on, the display-wake command gets missed and not repeated despite further mouse/keyboard use, and so the monitor never gets the request to wake up. Continuing to use mouse/keyboard beyond doesn't help, the monitor stays down in standby. Power cycling the monitor at this point does nothing, either.
 
I continued this test by then backing off mouse/keyboard input and not touching anything else nor power cycling the monitor, waited out the sleep-timer when the display would be put down into standby (even though the display was still in standby), and then I moved mouse/keyboard to trigger another wakeup event -- the monitor lights up to a black screen as if it received the request, but all it is is a lit black screen. So it's like the display gets "halfway" woken from standby. I then backed off the mouse/keyboard again and waited out the standby timer again. Then when I use mouse/keyboard, the display finally gets the wakeup call to pull it all the way out of standby, the desktop finally appearing.
 
If I merely power on my secondary HDMI monitor after this has happened, it must trigger another driver display-init loop, detecting and reinitializing displays, sending wakeup signals to both.

I have a similar problem.
 
Got an RTX 3080 FTW3 a month ago and I have a LG TV screen on HDMI port and a LG PC Monitor on Displayport. 
 
If Windows turn both of them off after let's say 20 minutes when I move my mouse the DP monitor goes on and I see a black screen.  If I turn on the HDMI TV the windows desktop appear on the PC monitor.  Been testing on all DP port from the video card and it does the same everywhere.  I can't even control my PC from distance with this bug because the only thing I see is a black screen.  The only solution I have for this right now is to turn off monitor sleep mode in Windows and put a blank screen saver instead so my PC monitor never shut down and even if my TV is turned off it will still works when I move my mouse.  Been searching a lot about this and only found this post and we both have the same video card (3080 FTW3) so OP did you found out what the problem was ?  Before I had an RTX 2070 witht he same TV / PC Monitor and it was working fine
 
Thanks

I'll test that but my PC is on 24/7 so I don't know why Fast Startup would help this
 
I'll try to explain better sorry for my english.  Before I go to sleep I turn off my TV and let my PC monitor ON.  It goes to sleep after 20min (Power & Sleep in Windows set to turn off monitor after 20mins).  When I come back to my PC the next day or I try to control my PC from another PC I get a black screen.  When I move my mouse I see the PC monitor powering on but the screen is black.  The only way to make my PC monitor works again is to power on my TV that is on HDMI port.  If I disconnect the HDMI TV from the video card when I come back the next day evrything works fine.  So if my TV is 100% turn off my PC Monitor will never goes back from sleep 100% .. it turns on but only get a black screen.
 
Thanks