I switched to a new phone, LG G4 running lollipop and noticed that I can no longer connect to my services remotely.

I restored from a backup on the older phone, Moto X running KitKat.

In the settings I have both the local ip and the remote url through duckdns dynamic dns service.

While I'm on Wi-Fi on the local lan, it takes 5 or 6 seconds to pull up sab, but it eventually does. Remotely, none of the services are reachable.

In the web browser I can reach all services locally or remotely in less than a second on the same phone.

Any way I can produce logs?

I have a suspicion that it is always trying to connect to the local ip. I connected to my home vpn over mobile data connection and voila, nzb360 connects right away (wifi not connected at all). When I disconnect the vpn, no connection.
My guess is something to do with your wifi / SSID settings. That's what nzb360 uses to determine the switch between local/remote