When, if ever, do they close [as in you can no longer buy from it]?

I don't believe they do close. They've been open since they were introduced last year.

No, they are open year-round :)

I believe that they have stayed open permanently since they were created. I don't think you'll have to worry about them closing.

They do not close. If you have the Trinkets you can shop from there year-round. =)

Awesome, thanks everyone! :]