Very well guys,

I was able to solve my problem.
I feel happy because I do not have great knowledge of this area, only determination.
After finding the problem, quoted in the post above, I solved the problem by putting a command at boot:

Echo "power on" | Bluetoothctl

Every time you start the machine bluetooth devices start normally.
Sorry for my bad English and sorry for the posts in a row.

Problem solved.

Links that helped me:
https://wiki.archlinux.org/index.php/bluetooth
https://forum.recalbox.com/topic/3206/bt-controller-does-not-autoconnect
https://github.com/recalbox/recalbox-os/wiki/Add-your-own-startup-script-(EN)
https://raspberrypi.stackexchange.com/questions/44520/bluetooth-autoconnect-on-reboot-car-setup-with-scripts