1. Open MuseScore.
2. Open score.
3. Enable Script Debugger .
4. Quit MuseScore (in order to show Script Debugger).
5. In MuseScore (still open, it hasn't quit), disable Script Debugger.
Result: Script Debugger is still there.
Using MuseScore 1.0 and 2.0 Nightly Build (4338) - Mac 10.4.11.
Comments
This is also on purpose. If you close the debugger, it will stop on the next plugin and so, until there is no more plugins to debug.