This occurs when trying to run Brackets on Debian 7 (Wheezy). There is a known issue (which is fixed in release 0.43) that if HTML file is in project tree (i.e.
not in Working Set), then element highlighting stops working after switching to a CSS (or other? The workaround is to double-click HTML file so it's added to the Working Set.
As noted above, live HTML updating is disabled when using your own custom local server.
Brackets is verified with the current stable Chrome.
In that case, re-installing Brackets should fix the problem.
If you had previously used Brackets, your cache may have information that is conflicting with the most recent version. Please verify that you've downloaded the correct build. Some (but not all) Live Development features require a node server, which means being in the current project, so make sure the files that you want to use with Live Development are in the current project.
See issue #7126 for an illustrated description including the line number and icon coloring.
Other known issues: dialog (see How to Use Brackets for details).
Another option is to use a tool such as Revo Uninstaller to uninstall Chrome.
Try leaving an extra blank tab open in the instance of Chrome that is launched by Live Preview.