If Time Machine detects corruption it will lock the backup to preserve its contents, rather than attempt to create another backup which is likely to fail, possibly leaving you with no backups.
The ideal solution is to obtain another backup drive before attempting to continue to use the existing one. Reformatting it is likely to work, perhaps for a long time, but it is 100% certain to fail again. When drive failures become intolerably frequent throw it away.
Refer to If you can't back up or restore your Mac using Time Machine - Apple Support.