What is the appropriate action to take if a sum of money was mistakenly transferred to someone's account, and it became impossible to return it to the transferring entity due to their unresponsiveness?

Your duty is to return these funds to their owners. There is no blame upon you for waiting as long as they have informed you that they will retrieve them. Be aware that this money is a trust with you, no matter how long the waiting period, and whenever its owner requests it, it is obligatory to return it to him.