I have a solution that worked for me(so far.. just got it working).
This is for the Ps4 but don't see why it won't work for xbox since it appears to be a server side issue and not on your end. Something is getting in the way and you must disable it from within your NHL 15 game. Very easy.
Go to SETTINGS
Go to ONLINE SETTINGS
Go to PRIVACY SETTINGS
Change your Privacy Setting to NO (what this does is it disables information from being sent to EA [has no affect to you, except for apparently getting in the way of the servers], and this isn't the first time I have encountered this issue on different systems and games and not the first time this has worked)
That should do it, it did for me. Press back and go into Origin Account Info, this is the first test to see if it worked. If your PS4 displays a message saying Gameplay Recording Stopped or something along those lines, it should show you info for your Origin Account(assuming your logged in already.. mine was apparently)
Before I changed the Privacy setting Origin Account Info said connecting and then the login error appeared, same as with any online features in the game. I went to VS. Mode and it connected immediately.
Give it a shot, hope it works! Let me know if it does!