You don't have to restart the Node Inspector process itself when the debugged process was restarted. All you need to do is reload the browser tab with Node Inspector GUI.
I am afraid there is no easy way at the moment for automatically reloading the Node Inspector GUI page when your debugged process is restarted. It is probably possible to perform some kind of active polling in Node Inspector backend, but that's a feature that would have to be implemented by somebody.
Depending on what part of your application you are debugging, you might find useful the feature "Live Edit". It allows you to edit your code from Node Inspector, save the changes to the Node/V8 runtime and possibly back to disk too. That way you don't have to restart the debugged process after you made your changes.
This feature has been implemented in Node Inspector and released in v0.7.0. See issue #266 for more details.
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