I was using a PS4 with JP 4.4.1 and it paired and would connect just fine even after a reboot or a start up.
However, with JP 4.5.1 after startup or a reboot, the PS4 will connect and then disconnect.
Yes, I reset my PS4 when moving up to JP 4.5.1 and re-paired it with my Nano.
I have used the Ubuntu Desktop as well as bluetoothctl to pair and connect my PS4 to the Nano.
If I turn the PS4 off and then turn it back on, it will connect with the Nano and then disconnect consistently.
If I run bluetoothctl from the CLI and turn scan on, the PS4 will connect and if I turn it off and then back on again, it will connect, then disconnect. If I try to connect a second time, it will connect and stay connected until a reboot.
It seems that bluetoothctl must be running after either a startup or a reboot to be able to get the PS4 to connect to my Nano. Very strange.
Presently the Ubuntu 18.04 that comes with JP 4.5.1 is running bluez 5.48 Oubuntu3.4 which is somewhat old.