The problem is most likely the \1, which is not repeating the first capture as I suspect you want. You may want to do something like:

use strict;
use warnings;

my $matchDate = qr/(\s*\d+th\s+\w+\s*)/;

while (<DATA>) {
    next unless /$matchDate\s+-\s+$matchDate/;
    print "Matched: $1 - $2\n";
}

__DATA__
5th April - 12th April
[download]

Prints:

Matched: 5th April - 12th April
[download]