Numerous users have been tweeting at the Ask PlayStation Twitter account to inquire why they can’t appear offline on their PS4. We’ve verified these on two PS4s ourselves. When going to your profile and selecting “Appear Offline,” the system does nothing and remains defaulted to the online option. If users were set to appear offline before logging in, or if you select “Log in with [Appear Offline]” then the system will switch the user to online upon logging in to the PSN. These are just a few of the complaints about PS4 appear offline functionality being broken.

@AskPlayStation why cant i appear offline"
? Henry smith (@Henrysm56883415) November 28, 2017

@AskPlayStation Appear offline option is not working for me. I click it and my online status still says online. ? Ghost (@GHOS777) November 28, 2017

@AskPlayStation the Appear Offline buttom is not working. Please fix this.
? ??? (@Kitsun8) November 28, 2017

@AskPlayStation I cannot set my status to Appear Offline on PS4. Tried restarting my console and disconnecting and reconnecting to internet. Still stays online. Restarting router not an option. Please help.
? Poofesure (@Poofesure) November 28, 2017

There are even more users reporting the issue if you search “appear offline” on Twitter. Ask PlayStation has been particularly unhelpful on the matter, replying to afflicted users with the PS4 equivalent of “did you turn it off and back on again"”...