If you really want a regex, this might do the job. I have omitted the date comparison code (Left as an exercise for the reader). Try this:

#!/usr/bin/perl

my $file = shift;
my $dDate = shift;

open (IN, "$file") or die "Couldn't open file: $file for reading\n";

my $slurp = join('',<IN>);

close(IN);

while ($slurp =~ /(<DAY DATE=\"(\d?\/\d\d\/\d\d\d\d)\">(.|\s)+<\/DAY>)/){
        # $1 Contains the whole match now.
        # $2 Contains the date in the current match.
	if(isOlder($dDate, $2)){
		$slurp =~ s/$1//g;
	}
}
print $slurp;

sub isOlder{
	#implement your own date compare
	return 1;

}

I used the XML text from your message and put it in a file called test.txt. Usage was: tester.pl test.txt '04/24/2001'

You may have to play with it a bit since it is currently too greedy (it substitutes with "nothing" more than I want), but I think this should give you a good start. Good Luck.

-Matt