This usually happens when RetroArch keeps control of the gamepad after it closes, so BigBox doesn’t get the controller back.
Try these steps:
In RetroArch, make sure you fully quit RetroArch (not just “Close Content”). Use “Quit RetroArch” so it releases the controller.
In BigBox/LaunchBox, enable the option that closes the emulator process on exit (force close on exit), so RetroArch can’t stay running in the background.
If you use Steam Input for the DualSense, turn it off for RetroArch and BigBox, or make sure only one of them is using it. Conflicts can cause the pad to stop responding.
Try switching the controller driver in RetroArch (XInput vs SDL) and keep it consistent with what BigBox expects.
As a quick test, exit RetroArch, then check Task Manager and end any remaining RetroArch process. If the controller works immediately after that, the issue is RetroArch not exiting cleanly.
If you share how you launch RetroArch (standalone, Steam, or through a launcher) and which input driver you selected, it’s easier to narrow down.