Sometimes after my computer is running for awhile, my GPU just stops running. In nvtop I can't see my GPU and only see my CPU. My CPU utilization goes through the roof as it tries to render everything (when this happened last night I could see there was some chrome render process that uses like 750% CPU in htop). The "Geforce RTX" light is still on when this happens. Also, my monitors are plugged in through the GPU, not the motherboard.

This wouldn't be a huge problem because restarting fixes it, but my computer is set up at home and is accessable via ssh. If I need to restart my computer, my GPU isn't recognized until AFTER I am signed in via the Desktop GUI. So if I'm away from home and need to reboot my computer (I do this via sudo reboot), I have to call my roommate and he has to walk over to my computer and sign me in. Then I can see my GPU in nvtop once he signs me in.

My system has a Nvidia 3080 Ti and I'm running Ubuntu 22.04.2 LTS

Check dmesg and /var/log/Xorg.0.log for errors.

But the most likely culprit is a HW issue: either your GPU is overheating (quite common problem this generation: some GPUs were sold with incorrectly-spread thermal paste; repasting fixes it) or the PSU can't provide enough energy and it goes down after the GPU asks a power spike (transient spikes is also a common problem for the 3000 series)

Login via CLI

In ssh you can try:

sudo service lightdm restart
sudo service gdm3 restart
sudo service sddm restart

Which one you need depends on your Desktop Manager.