Apple doesn't respond. Your reports go into a general reporting system so that if there is a systemic problem and lots of folks submit the same report they know to do something. For an individual report they don't respond.
However, setting the display not to shut down may or may not prevent the machine from shutting off. You need to set the computer to never shut down, too. Same place in System Preferences as the screen options.
It sounds like your shutdowns are occurring due to crashes or perhaps a kernel panic? You don't normally get a notation to send a report to Apple for normal shutdowns. Go to your logs and post the shutdown log here for us to look at.
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