Have you been in contact with your host (to access the error logs)?
The support of the hosting provider should be able to see unusual spikes.
If you don't have any special agreement concerning error-assistance with them, they should at least be able to help to pinpoint the problem.
Another guess: Did you scan for malware? Just to be sure that there is no script (on your server) being executed or being accessed from external sources every 12 hours.
https://wordpress.org/plugins/sucuri-scanner/