Will an aqueous sodium hydroxide solution degrade over time?
Usually, the biggest problems with preventing a sodium hydroxide solution from changing in $\ce{NaOH}$ concentration, or pH, over time are adsorption of $\ce{CO2}$ from the air, and evaporation of water via permeation through the container holding the solution.  

If we can really say that it is inside a closed system as you've specified, then any degradation over reasonable time-scales (i.e. months to years) should be negligible.  

However, you need to be sure about your "closed system". Is it glass, which could slowly react with the $\ce{NaOH}$? Is it a plastic that could be slightly permeable to water vapor, air (and thus $\ce{CO2}$), etc.? Is it, heaven forbid, a metal that would react and degrade your $\ce{NaOH}$? You need to think about these things at every contact point (vapor or liquid) throughout your system.