To track this down better, maybe you can dump the object(s) in question at strategic places of the lifetime of your program. Maybe you get lucky and find that no_DESTROY gets reset/lost somewhere or a place where another object holds on too long to the object in question.

Note that closures are notorious for holding on surprisingly long to objects:

sub make_frobnitzer {
    my( $self )= @_;

    $self->{on_error}= sub {
        $self->error_on_frobnitz( @_ );
    }
}
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In the above case, $self will live until global destruction, because the on_error subroutine closes over $self.