foreach $case (@items)
{
    chomp($case);
    
    @values = split(/\|/,$case);

    $driveltr            = $values[0];    
    $dira                    = $values[1];
    $dirb                    = $values[2];
    $unique_id        = $values[3];
    $case_num            = $values[4];
    $case_part        = $values[5];
    
    $tester = length($case_part);
    
    $zip_file_name = "$file_path/$case_num.zip";
    
    if ($tester > 0)
    {
        $file_name = "$unique_id-$case_num-$case_part.tif";
        $file_to_zip = "$file_path/$unique_id-$case_num-$case_part.tif
+";
        
        #$zip_file_name = "$file_path/$case_num-$case_part.zip";
        
    }
    else
    {
        $file_name = "$unique_id-$case_num.tif";
        $file_to_zip = "$file_path/$unique_id-$case_num.tif";
    }
    
     print "to that zip file I will add $file_name\n";

    my $zip = Archive::Zip->new();
    my $member = $zip->addDirectory( 'dirname/' );
    #$member = $zip->addString( 'This is a test', 'stringMember.txt' )
+;
    #$member->desiredCompressionMethod( COMPRESSION_DEFLATED );
    $member->desiredCompressionMethod();
    $member = $zip->addFile( "$file_to_zip", "$file_name" );          
+        
    die 'write error' unless $zip->writeToFileNamed( $zip_file_name ) 
+== AZ_OK;    
    
    #sleep(2);
}
[download]

it's because my $zip = Archive::Zip->new(); AND writeToFileNamed are both in the loop .. so you're not appending to the same zip object -- you're creating, adding one file, writing out to disk, and then $zip is destroyed before the next iteration. Move my $zip = Archive::Zip->new(); to before the forloop, and the write to after.

my $zip = Archive::Zip->new();
foreach $case (@items) {
  ...
  my $member = $zip->addDirectory( 'dirname/' );
  $member->desiredCompressionMethod();
  $member = $zip->addFile( "$file_to_zip", "$file_name" );            
+   
}
die 'write error' unless $zip->writeToFileNamed( $zip_file_name ) == A
+Z_OK;
[download]

btw, are you doing use strict; and use warnings; somewhere in your code?