It was actually an LGO decision that set the limit at 3 days. It isn't available on the LGO's website, but the reference is 99C01876.
The judicial review that is often mentioned essentially established that an offer made in error can be withdrawn if the withdrawal happens quickly. The LGO decision established that the admission authority only has 3 days to withdraw the offer and is therefore the more significant of the two decisions, but I would mention them both.
The appeal panel should be aware of this, but it depends on how well they have been trained. In case they aren't, the broad outline of this case is that the head teacher of a school offered places to 5 pupils incorrectly. The LA found out and wrote to the parents 3 days later, withdrawing the offers (so the parents received these letters 4-5 days after the offers were made). The parents threatened legal action, and the LA consulted a barrister, who advised them that the parents would win and that withdrawing the place after this time would be regarded by the courts as an abuse of power. The LGO agreed with that assessment.
The reason offers made in error must be withdrawn quickly is that, if they aren't, parents may well have bought uniform, entered into childcare contracts, etc., based on the offer that was made. If they have done so and the offer is then withdrawn, they may not be able to get their money back.
Note that the clock starts ticking when the offer is made, not when it is accepted. If the appeal panel understand the precedents properly, the fact that you delayed accepting will not be considered relevant.