I also have this issue and put a ticket into support with https://gearboxsoftware.zendesk.com/hc/en-us just like @hakunaro has done. Currently because I am a new player the game is offering less content than a demo would typically have, because this issue also makes it impossible to progress through the story. It took me around 10 attempts of the story prologue before it allowed me to start playing Episode 1: The Algorithm, now I have replayed The Algorithm over 5 times and it has not saved any of my successful runs, including a run on Hardcore mode that I did with friends in co-op. It is disheartening to complete something to then have the game give the error afterwards. Support in my ticket haven’t responded in over 2 days now and their last message is an automated one that doesn’t give any guarantee about there being a fix.
Since Sunday, November 17th 2019 I have only had 2 matches that I have played on the game save any of my stats, although I have played well over 30 matches across the PvP and the campaign. I’m tagging @Noelle_GBX and @VaultHunter101 to this post in hopes that the issue can be escalated and a resolution can be given to the issue, you are the staff members who have given responses to this thread so I hope that you can have an influence on the issue being fixed.
I have bought the season pass and feel that it is unfair that with the current state of the game, I am limited to only being able to play 1 story mission in the main campaign. My ticket number is: #196637 and I am willing to send any other information that may be requested of me. Thank you.
I am aware that this is an error that has happened in the past, so I hope that the same solutions that have fixed it in the past will allow it to be fixed in the present.