[markem]

Since it hasn't been addressed in quite this way, I'll jump in.

It appears to me that you are in the situation where the ambient RH in your house fluctuates, probably based on time of year. That you would have a problem holding RH inside your storage when the ambient RH is so low should not be surprising. You notice this because the ambient RH isn't consistent enough for you to use only a single approach to how you maintain the RH inside your storage year round.

First, realize that almost no cigar storage container will have a perfect seal. I recall taking a class in college called "The Viscosity of Solids" which hurt my head but hammered home the impracticality of trying to perfect seals except where it was necessary to sustain life. Second, since some exchange will occur between the ambient environment and the storage environment, one can expect to see a larger change to occur, in this situation, when the differential gradient is steep, such as you describe.

Adding more beads or kitty litter or what-have-you may be a perfectly reasonable solution that gets you past the dry times (I am assuming that your beads are quite dry right now). However, you can also run a small experiment for almost no money. Get a small, nonporous container and clean it thoroughly with hot, soapy, distilled water. Rinse it completely with distilled water. Put some distilled water in to the container and put it in to your storage. This is, in effect, supplementing your passive humidification (beads) with a simple form of active humidification. The beads will let you know when you can remove the water container.

I used to do that for my coolers in the winter. Saved me loads on beads.

An alternate is to have a spray bottle of distilled water that you use to mist the inside lid of the storage on occasion. Don't mist the boxes or sticks. Much more work, but same concept and doesn't take any space.