Maybe the (Sybase) database driver doesn't like only half-fetching the resultset? Have you tried fetching the complete resultset and then issuing your second query? Something like:

my $prod_dbh = DBI->connect_cached('DBI:Sybase:database','web_','web')
+ || die "Couldn't connect to DB!\n" . DBI->errstr;
my $parent_sth = $prod_dbh->prepare_cached('select * from table where 
+id = ?');
$parent_sth->bind_param(1,$id);
$parent_sth->execute();
my $parent_data = $parent_sth->fetchall_arrayref();

...

my $child_sth = $prod_dbh->prepare_cached('select * from table2 where 
+id = ?');
$child_sth->bind_param(1,$parent_data[0]);
$child_sth->execute();
my $child_data = $child_sth->fetchall_arrayref();
print Dumper($child_data->[0]);
[download]

Of course, with your statement handles named $parent_data and $child_data, maybe you are trying to fetch data in a parent/child relationship where you instead could be doing an SQL JOIN between the two tables to issue only a single query?

select 
       parent.*
     , child.*
  from table parent
  join table2 child on (parent.id=child.id)
 where parent.id = ?
[download]