You are not banned from Fortnite - The Verge

According to the game’s official status account, “Players who see a message saying ‘You do not have permission to play Fortnite’ or ‘Your account no longer has play access to Fortnite’ because of this issue are not banned from Fortnite.”.

Epic Games is currently investigating “issues related to kicks and logins.” The developer has promised updates when the issue is resolved

“As we work to resolve this issue, we have entered server downtime,” the developer said