You need the g (global) modifier and possibly the s (ignore line ends) modifier. You also need to remove the $ (end of pattern match). You also need to match "Perl Party".

Test code would look something like this:

use strict;
use warnings;

my @dates;
my $string = do {$/ = ""; <DATA>};

while ($string =~ /\b(\d{2})-(\d{2})-(\d{4})\sPerl\sParty/g)
  {
  push @dates, "$1\.$2\.$3";
  }

print join "\n", @dates;

__DATA__
All kinds of text 01-01-2003 Perl Party more text 01-01-2004 Perl Part
+y
and even more text 01-01-2005 Perl Party
and finally some other date 01-01-2006
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