When using Safari Web Inspector to view the Network Log, the log is reset upon navigation, i.e. navigating to a different page clears the log.
In the Chrome Develope
This was just added to WebKit last week: https://trac.webkit.org/changeset/211451
You can expect it to make it into a Safari Technology Preview build soon. Once it's in a build, you can toggle preserving logs on navigation in the Settings Tab.