What time does AJHQ update? What I mean is what time do they add new items to stores?

There is no official time. They usually update when there aren't many jammers online, yet I'm confused AND surprised on why you didn't know. ;) Edit

As of current there is no set update time, although its been observed that they usually update when not many players are online. This is probably to prevent spam and lag on the servers. Edit

Although I have observed on my many nights of staying up late that they usually update around 4 - 7AM PST every other Thursday. Edit