I don't think your problem is with Class::DBI, it is with perl. You have two nested foreach loops, and both use $_. Try the following and see what happens:

foreach my $buechereien (@kk) {
        last if $i++ > 10;
        printf "%02d. %s\n", $i, $buechereien->customer->plzort;
        # This is where the problem occurs:
        foreach my $kontakte ( $buechereien->kontakte ) {
                printf "  %s\n", $kontakte->aktion_kurz;
        }
}
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- Cees