Short answer. Yes, if he is keeping it for free and has justifiable reasons for not keeping it any longer. He may return it even before the agreed date, and if you refuse to take it back he can ask the court to let him consign it. A paid keeper cannot do this.
What the law says
Unless the deposit is for a valuable consideration, the depositary who may have justifiable reasons for not keeping the thing deposited may, even before the time designated, return it to the depositor; and if the latter should refuse to receive it, the depositary may secure its consignation from the court.
Civil Code, Article 1989 — Depositary's Early Return. Read the full provision →
The favour can be withdrawn; the paid service cannot
Everything in this article turns on the opening words. Where someone is keeping your property for nothing, the arrangement is a favour, and the law does not make him a prisoner of his own generosity. Where he is being paid — a storage company, a warehouse, a bonded facility — he sold you a term and has to serve it out. Read your paperwork with that distinction in mind, because it decides the answer before any discussion of reasons begins. A relative minding your appliances while you work abroad and a warehouse holding your stock are in completely different positions, however similar the two situations feel.
What counts as a justifiable reason
The Code does not list them, and it does not need to. What it requires is a reason a fair-minded person would accept as genuine rather than a change of heart: the keeper is moving house or losing his storage, the item has begun to need care he cannot give, his circumstances have changed so that holding it exposes him to risk, or the deposit is interfering with his own use of his premises. What it is not is a bargaining tactic — announcing an early return to extract money that is not owed, or to settle an unrelated quarrel, is not a justifiable reason for ending the arrangement.
If you refuse to take the thing back
This is the part people overlook. A depositor who simply will not answer the phone does not force the keeper to go on holding the property indefinitely. The article lets the keeper secure the consignation of the thing from the court, which means depositing it with judicial authority so that it is no longer his problem. He is then discharged, and the property waits for you on the court's terms rather than in his garage. Refusing delivery therefore does not preserve your arrangement; it just moves your things somewhere less convenient and adds a proceeding neither of you wanted.
Handling the return well
If you are the keeper, give notice in writing, state the reason plainly, propose a date and a place, and keep proof that the notice was sent. If you are the owner, treat the notice as real and collect the property, taking photographs and signing a receipt that records its condition at handover. Both sides should settle any expenses at the same time, since a keeper is ordinarily entitled to be reimbursed for what he spent preserving the thing. An orderly handover, documented on the day, prevents the far uglier argument about what condition the item was in when it changed hands.