I'm with moritz: if the file is not too big, reading it into a single scalar string is the way to go (once you actually do read the file). But unlike moritz, I would split on the date pattern, using parens in the split regex so that the dates get returned along with the stuff around them:

use strict;

my $text = do { local $/; <> };
my $date_rgx = qr/\d{4}-\d{2}-\d{2}/;

my ( $date, $text ) = ( '', '' );

for ( split /\n($date_rgx)/, $text ) {  # capture the date (but not th
+e preceding \n)
    if ( /^$date_rgx$/ ) {
        $date = $_;
    }
    elsif ( /\bkeyword\b/ ) {
        print "$date$_\n";
    }
}
[download]

(not tested; updated to use a variable other than $_ to hold the original file data, and avoid possible confusion in the "for" loop.)