I would keep my (business) logic as simple as possible:

use strict;
use warnings;

while ($_ = getrecord()) {
    print "----RECORD----\n$_\n";
}

my $saved_header;
sub getrecord
{
    my $text = $saved_header;
    $saved_header = '';

    while (<DATA>) {
        if (/^====[^=]+====$/) {
            $saved_header = $_, last if $text;
        }
        $text .= $_;
    }

    return $text;
}

__DATA__
====header info====
0
10 to 50 line of text and
numbers with ==== irregular ====
formatting
====header info====
10 to 50 lines of text and...
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