Pretty self-descriptive. When the weekly update comes out, tents disappear after the update is applied if they are pitched. If they remain in the inventory, then they're retained.

This causes a couple of very tiresome problems:

1. Everything you've collected that you want to keep (including your tent) at your tent-base has to be cleared out every week or you lose it.

2. Where this really becomes a problem is with Big Military Tent (not sure about other tents) where you can only choose between the tent or a backpack. Which means the purpose of the tent becomes largely self-defeating (why collect a bunch of stuff, when you will only have a jacket, pants, and vest worth of slots to carry things with if you want to keep your tent).