My answer is that in the bottle, there is no room for the solvents to evaporate and therefore the enamel will not thicken as they are trapped in the bottle. Open to the atmosphere the solvents escape which alters the formula of the polish and allows the necessary solvents that keep the polish 'open' to escape.
Drying is a process whereby we wait for the solvents to evporate which is part of the drying process. Lack of oxygen on the surface of the polish helps the solvents to escape more quickly from the enamel.
In the bottle when it is closed, there may be a lack of oxygen, but there is nowhere for the solvents to escape, so the polish keeps viable for longer. Given enough time, the polish would dry in the bottle too but it would be a long slow process indeed in the small amount of room available. Polishes that are nearly used up will deteriorate over time as there is more room in the bottle for solvents to dissipate.
The benefit of the polish being thixotropic is that when not agitated, or just standing unused, the polish sort of goes into a state of suspension until the polish is agitatated which allows the solvents to evaporate even more slowley than in polishes that are not thixotropic. This is the reason CND polishes last in good condition for so long.
I hope this helps.