I saved file FlameChart.js as .allow-devtools-edit into a folder. The next times when I save the file it is actually saves as '.allow-devtools-edit' and after reload I see unchanged version of the original 'FlameChart.js" file. Yeah, I understand that I shoot into my feet myself. But the web developer has no chances to understand what is going on. I think that we have to change the tab name according to the new name of the file because it is the default behavior of the editors.
Closing as invalid, as this bug pertains to the old inspector UI and/or its tests. Please file a new bug (https://www.webkit.org/new-inspector-bug) if the bug/feature/issue is still relevant to WebKit trunk.