Postgresql | No space left on device
Most likely there are some queries that create large temporary files which fill up your hard disk temporarily. These files will be deleted as soon as the query is done (or has failed), so the file system has enough free space when you look.
Set log_temp_files = 10240
in postgresql.conf
(and reload) to log all temporary files exceeding 10 MB, then you can check the log file to see if this is indeed the reason.
Try to identify the bad queries and fix them.
If temporary files are not the problem, maybe temporary tables are. They are dropped automatically when the database session ends. Does your application use temporary tables?
Another possibility might be files created by something else than the database.