Such boxes are great for temporary display (for expo or some event) but for storage you should avoit it.
You will kill your plaques on long term because you will accelerate the natural chemical degradation process that occur.
Most plastics contain organic polymers and they are degraded naturally and you can' t stop it but in a closed environnement like a box you concentrate vapour of solvent plastic.

Please note that all old plaques are fragile especially the lunette. Here are few examples:
First the lunette is sticky like this one http://plaques.marlowcasinochips.com/UK/106_Crockfordsplaque100offwhite.jpg
Secondly the lunette collaspe like this one http://i.ebayimg.com/00/s/MTA2NlgxNjAw/$(KGrHqJ,!i!F!OoM0TNiBQQww4SgTQ~~60_12.JPG
and finally is crackled (with global distorsion)

To conserve your plaques you should:
- storage temperature ~18° Celsius
- don't let the plaques to contact each other directly (and most generally no contact with another plastic)
- use a storage with some ventilation
- no contact with metal
- no contact with material painting
- and most important: Keep your plaques in the dark whenever possible! Avoid any light espacially natural light. UV kill all plastics on long term.

Look at this picture on the left the worst thing to do: put a plaque inside a closed plastic bac... they won't live long
http://img15.hostingpics.net/pics/84499712000371.jpg

(sorry for bad english )