use strict and warnings. This will show you that your $birthdate variable is out of scope Why do you think there is a problem with your regex?

use strict; 
use warnings; 

my $text = 'birthdate1234zodiac';
if ($text =~ /birthdate(.*?)zodiac/i) {
    my $birthdate = $1;
    print "$birthdate\n";
}

__END__

prints:
1234
[download]

If that's not the problem, then you should show us a small sample of your input file.

You would also benefit from running your code through perltidy and perlcritic.