Safari Developer Tools: Preserve Network Log on Navigation

In Safari 11.1.2 this is a setting on each tab under the checkbox "Preserve Log"

Note that if your Web Inspector window is too narrow to show all options, you'll have to expand it until it is wide enough to display the Preserve Log option, as mentioned in an answer by ShortFuse.

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In Safari 11 this was in the Settings panel under "Network: Clear when page navigates", and it's sister setting "Console: Clear when page navigates".

There is a Preserve Log option in Network.

The problem is that if your window is too narrow, it disappears and Safari gives you no indication that it's there. Resize your Web Inspector window to be wider.

(That was a fun one to figure out!)