Here is a bit of information on the subject that I dug up. it makes for an interesting read. I'm sure a couple of brothers on this forum have probably seen this before.
"I always stored my cigars in Ziploc bags. As do many other Hong Kong old timers.
There are 2 reasons:
1. Fermentation is oxygen dependent. (See pictures 1 and 2.) Less oxygen, slower fermentation, more time for chemical reactions, more complex aromas, better aging results.
2. Oxygen in large quantities, as in wines, destroys delicate aromas. The Cubans must have discovered this ages ago. The flap covering the cigars when you open a dress box, the “Bofetón”, prevents air entering the front side of the box, but there is no protection for the 2 remaining sides. But to be fair, the entering of oxygen is most aggressive in the front side.
Some say this is a Hong Kong invention, as you don’t see this practice done by the British, who have a long history in aging cigars.
People are mistaken. Cigars stored in UK cigar shops are not wrapped, as they must be subjected to periodical inspection. (Some are, by special instruction from customers.)
But for cigars in the private inventory of huge collectors in Britain, many are wrapped in wax paper. Many are still wrapped when they appear in Christie’s auctions.
The reason you don’t see too many wrapped original boxes in Christie’s auctions is because the vendors chose to unwrap the box. People do not like to buy cigars without seeing them. Wrapped boxes typically realise less money than open boxes."