My guess is, that one of your filehandles is not in binmode. Try if this makes a difference:

use MIME::Base64;
use Fatal qw/open/;

my ( $buffer, $file_data );
open my $reader, '<:bytes', "TEST.gif";
while ( read( $reader, $buffer, 10 * 57 ) ) {
  $file_data .= decode_base64( encode_base64( $buffer, '' ) );
}

open my $writer, '>:bytes', "TEST_base64.gif";
print $writer $file_data;
[download]