Mine now shows complete... So it DOES update before shippingNo, but I find it's usually up a few minutes later.
...and down a few minutes after that.
I'm wondering if the "Server is down" message is bogus and is the result of some other connection issue. Anyway, others have pointed out that their jeep still shows an active recall notice despite having shipped from the yard, so I'm no longer using it as a clue as to when my jeep will ship.