I discovered a hard to diagnose issue which is that on one of my Drupal 7.56 sites, the watchdog functionality is no longer working. I can confirm that I can log and generate PHP errors (using error_log and even TRIGGER_ERROR) is working but watchdog is not. I noticed also that the watchdog table is empty in the database.
I created a fresh install of Drupal 7.56 in another directory to test and can confirm that in the fresh install watchdog is working and the watchdog table has entries in it.
I have replaced the dblog module in the site where watchdog is broken and also compared the system.sql table for both sites but the configuration is the same.
Any ideas on where to look to debug why a site is not writing any log entries? Admin -> Reports -> Recent Log entries is also always empty.