I have the same problem after I updated iThemes security few weeks ago.
The following messege shows every day at least a few times: “Fatal error: Allowed memory size of 268435456 bytes exhausted (tried to allocate 83368992 bytes) in plugins/better-wp-security/modules/free/backup/class-itsec-backup.php on line 148”
My php memory limit is 268 MB and I am using only 64.54 MB, I already contacted my hosting provider and they increased the limits.
Does anyone have any idea how we can deal with this problem?