Short answer. Yes. Article 1979 makes a depositary liable for loss through a fortuitous event — like a fire — if he delays returning the thing. Delay in returning it after you asked for it back falls squarely within that rule, so the fire does not excuse him from liability for the loss.
What the law says
The depositary is liable for the loss of the thing through a fortuitous event: (1) If it is so stipulated; (2) If he uses the thing without the depositor's permission; (3) If he delays its return
Civil Code, Article 1979 — Liability for Fortuitous Loss. Read the full provision →
The general rule this article overrides
Ordinarily, a person who loses something through a fortuitous event — an occurrence like a fire that was not caused by anyone's fault and could not reasonably have been avoided — is not held liable for it. That is the general rule for obligations that could not be performed because of an event beyond anyone's control. Article 1979 carves out four specific situations where a depositary loses that protection and becomes liable for the loss anyway, even though the fire itself was not his doing.
Delay in returning the thing is one of the four
Article 1979 lists delay in returning the thing as one of the grounds that makes a depositary liable for a fortuitous loss. Once you asked for your property back and the depositary failed to return it within the time you specified, he was already in delay with respect to his obligation to return it. The article treats that delay as enough, by itself, to shift the risk of a later fortuitous loss onto him — it does not require that the delay somehow caused the fire, only that the thing was overdue for return when the loss happened.
Why the rule is framed this way
The underlying idea is that once your property should already have been back in your hands, it is no longer fair for the depositary to enjoy the protection ordinarily given for events beyond anyone's control. Had he returned it on time as agreed, the fire would likely never have reached your property while still in his custody. The article does not ask whether the depositary was careless in how he stored the item during the delay — the delay itself is what removes the fortuitous-event defense, regardless of how carefully the item was otherwise kept.
The other situations covered by the same article
The same article also removes the fortuitous-event defense where the parties stipulated that the depositary bears that risk, where the depositary used the thing without the depositor's permission, or where he allowed someone else to use it even if he himself was authorized to. Any one of these, on its own, is enough to make the depositary liable for a loss that would otherwise be excused. Delay in returning the property, as described here, stands on the same footing as those other grounds under Article 1979.