In order for a call to be recursive, the function must be called from within itself. You do not do that here. If you want to keep a recursive structure, you could do something like:

sub autoSubmit{
   print "Would you like the logs submitted? Y\\N?: ";
   my $autoSubmit = getInput;
   if ( (lc($autoSubmit) ne "y") and ($autoSubmit ne "n")) {
       print "You did not enter in Yes or No.  Please try again\n";
       $autoSubmit = autoSubmit();
   }
   return $autoSubmit;
}
[download]

However, recursion in this case seems like overkill to me, since you could just use a while loop to do the same thing:

sub autoSubmit{
   print "Would you like the logs submitted? Y\\N?: ";
   my $autoSubmit;
   while (1) {
      $autoSubmit = getInput;
      last if ( (lc($autoSubmit) eq "y") or ($autoSubmit eq "n"));
      print "You did not enter in Yes or No.  Please try again\n";
   }
   return $autoSubmit;
}
[download]

See last for some info on loop control.