Check out these two charts:
http://www.magnumsolvent.com/product...20Chloride.pdf
As AC has described, when the brine solution cools (in a regenerator or a heat store), especially when cooled from above 45 degC (around 115 degF), the calcium chloride has an inconsistent behavior as to when and how the dissolved, melted salts refreeze. Mainly, different crystals form at random.
To further complicate matters, the fractions which freeze first are less soluble in water. It works against someone using a sealed container for a heat store, because the dihydrate and tetrahydrate give up water molecules to solution as they freeze, effectively diluting the solution. The heat store engineers are all about the hexahydrate since its heat of fusion is the highest. More heat of fusion = more heat storage per unit of measure.
In a dehumidifier, this effect doesn't really affect much UNLESS the salt concentration gets upwards of 45% or so. As long as there is enough water in the solution, all the salt will remain dissolved in it. At sky high temperatures (above 250 degF at 40% concentration), the water will eventually boil out of the mixture due to vapor pressure. Due to this boiling, solutions of more than 69% cannot be achieved at atmospheric pressure. At around 320 degF, solid dihydrate separates from solution as a solid. The solution can never reach 70%.
If I were trying to make some sort of solar distiller/reformer outdoors, I could set up a still that would heat the pot or column to near 300 degF, evaporating and/or boiling the water out of solution. At or near 300 degF, the vessel could be drained into a cooler place (think ice trays) where the highly concentrated solution would refreeze, giving up gobs and gobs of heat in the process. This solid could then be used many ways. It could be recycled as desiccant. It could be used to heat water (just toss it in a container of pure water and it naturally warms the container as it dissolves). However, this is not a highly efficient process used just to dehumidify the air.