Long-term storage of Ascorbic Acid mixed with Sodium Bicarbonate
The reason that your solid mixture is clumping and hardening inside your airtight container is that the reaction between the two compounds is producing water as follows:  

$$\ce{C6H8O6 + NaHCO3 &lt;=&gt; NaC6H7O6 + CO2 + H2O}$$  

where $\ce{C6H8O6}$ is ascorbic acid.  

This reaction proceeds rapidly in the presence of excess water, which allows the reacting species to dissolve and thus have ready access to each other. This results in the observed fizzing from the release of carbon dioxide.  

In the solid phase, the initial reaction is limited to the surfaces of the particles coming into contact with each other. As the reaction proceeds, the once purely solid material becomes wet via the acid-base reaction producing water, and the remaining materials can somewhat dissolve, facilitating migration of the reacting species so that on a timescale of hours all of your material has reacted.  

Regarding the stability of storing the solid mixture vs. storing the solids separately, you are probably better off storing them separately until use. Both ascorbic acid and sodium ascorbate are susceptible to being oxidized by long-term exposure to air. Although water itself shouldn't act as an oxidant here, it could facilitate reaction with oxygen in the air in a similar manner in which it facilitates the acid-base reaction, as discussed above.