I have tried persistent stream key several times, but no matter, I always have to get a new key when starting a new stream.
Then I'd think something else is going wrong. Then again, I'm still on OBS Studio v25.0.8
I never had a problem with FB's Persistent key when I was using it. But again, it is generally consider poor security to utilize such, and one really shouldn't be monitoring one's own stream, so if you are there [FB Live Producer] already, why not use unique/new stream key.... so I won't comment further on Persistent Key use or problems.
Now, there was some PEBKAC on my part ... I'd log into FB/live/producer using a account A, and admin for the group streaming for. The default is a personal stream. More than once I'd overlook changing to Manage Page and switch to our Group Page, and when I'd start to get anxious as Scheduled stream was missing, or other, then I'd realize I'd erred and not switched to intended Group.
As a side comment on above, as mentioned we log in 1+ hour ahead of time to grab stream key, and test stream (to enable lots of troubleshooting time, if required). Typically, hitting Start Stream in OBS results in a preview video appearing at FB Live Producer with ~10-15 seconds, rarely a little longer and never a lot longer [I'd start troubleshooting after 30 seconds]. One other thing such an advance login/check of a Scheduled Video is checking if 'Scheduled Video' is missing (had that happen a couple of times... not sure if FB error or screw up by someone else within our Group), but also a chance to check (& update if necessary) stream settings [like not Ending, Adding Hosts, add Featured Link, etc well in advance of actual livestream meaning plenty of time for updates to propagate.