The Xbox controller was suspending and I had to unplug/replug it to have it back working. From TLP documentation it is simple to change the behavior.
Find the ID of the controller with lsusb command:
$ lsusb
Bus 001 Device 006: ID 045e:028e Microsoft Corp. Xbox360 Controller
Edit the file /etc/tlp.conf to add the controller to autosuspend blacklist:
USB_BLACKLIST="045e:028e"
After a reboot this specific device can not shutdown by itself and stays up all the time.