I experienced a performance drop after playing for a while with the console connected to the TV using a Bluetooth controller. After tweaking some settings and troubleshooting, I noticed that whenever the performance drop happened, quitting the game would show the console in rest mode with the MuOS screensaver active.
Changing the rest mode settings (either disabling it or setting the governor performance mode to ondemand) fixed the issue for me. I believe the console was mistakenly entering rest mode because it wasn’t registering direct controller input.