How can I recover a missing BTC from a correct transaction and who is the responsible for it?
Without your tx id it is hard to tell what exactly happened but usually you don't need to be worried. Your described scenario sounds like a "miner fee too low" issue, the transaction gets broadcasted successfully, thus Gatecoin or any other exchange believe the funds are out of their system, but then got pushed out from the mempool because other transactions have a higher fee. Such issue usually fixes itself once the fees on the network/mempool go lower. The transaction will be automatically re-broadcasted by the bitcoin node of the exchange and then gets included in a block and you get your coins on the receiving address.