Cigars won't stay humidified for very long at all outside of a humidor, no matter how tight the seal on the box. They will start to dry out within a day. Get them to a humidor. If you don't have one, you can use a Boveda Humidor Bag, which works very well. These bags come in a variety of sizes and are preloaded with a Boveda pack inside to keep your smokes properly humidified. Boveda says that cigars will keep for a minimum of six months inside one of these bags.
In a pinch, you can use a big Ziplock bag and put in a very small piece (two inches square, perhaps) of damp, not wet, paper towel to add some humidity.
Those general rules about how often you need to refill your humidification unit go right out the window. Fill it often, every day if your cigars aren't moistening up.
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