No, fully refundable fares are fully refundable at any time up to the flight. That's the whole point of a "fully-refundable" fare; it has no penalties for refunds. This is made pretty clear in the fare rules, and is the basic reason to buy full-fare tickets rather than discount fares (apart from the mileage bonus, I guess).
The 24 hour limit is for refunds on non-refundable fares. Most airlines will still let you cancel any ticket within the first 24 hours, even a discount fare (in the US, the DOT requires this for tickets booked at least 7 days in advance).
The 24 hour limit is for refunds on non-refundable fares. Most airlines will still let you cancel any ticket within the first 24 hours, even a discount fare (in the US, the DOT requires this for tickets booked at least 7 days in advance).