A maintenance plan does not overwrite the old backup file. It creates a new backup file, and then deletes the old backup file after creating the new one. It needs enough space for 2 backups files bacause of this. This is the safe way to do backups, because you always have a backup file on disk.

The solution is to make sure you have enough disk space for 2 backup files.

What is the size of your database. I know with 353 Gb available space the pointer I reference may not be the case.