The PS4 has an issue where you may be logged out of PSN with a message that some one else has logged onto your account.
Now normally this means someone else has your password and is trying to log onto PSN on another PS4, but if you’re definitely sure that your password belongs to no one but you, here’s a fix for that.
You need to set your clock to automatic.
If that doesn’t work change your password immediately and then try logging onto PSN.
Furthermore, if this issue isn’t fixed you need to contact customer support and ask them to deactivate all PS4s or do it via the Sony Entertainment Network website.
Let us know if you’ve managed to fix this issue.