Is it permissible for a charity to take a percentage of donations, and what is the ruling concerning orphaned funds accumulated by it due to the impossibility of transferring them to their rightful beneficiaries?

Charitable organizations act as agents, and they are required to adhere to what the principal specifies. If the principal does not specify, the agent is permitted to act in a manner that serves the best interest. It is permissible for them to deduct a percentage to cover administrative expenses if it is not possible to obtain these funds from other sources, and only to the extent needed. There is no sin upon the organization for delaying the delivery of dues to their rightful owners due to an excuse, and "Allah does not burden a soul beyond its scope." If you observe any shortcomings, inform the officials and advise them with wisdom and good counsel.