I am writing to apologize for the misplacement of [item] that was entrusted to me. I understand that this item was of great importance to you and that its misplacement has caused you a great deal of distress.
I take full responsibility for the misplacement of this item and I am deeply sorry for my negligence. I understand that this item was of great value to you, and I regret that I was not more careful with it. I am aware that I have caused you a great deal of inconvenience and I apologize for this.
I want to assure you that I am doing everything in my power to locate the item. I have been searching for it diligently, and I am confident that I will be able to locate it soon. In the meantime, I am willing to reimburse you for the cost of the item, if necessary.
Once again, I apologize for my negligence and for the distress I have caused you. I will do everything in my power to locate the item and to make it up to you. Please do not hesitate to contact me if there is anything else I can do to help.