Shards are always saving the world state. It takes about 10-15 minutes to complete, which is why time warps are next to non-existent when a shard crashes. If you mean when do they take down Test Center for maintenance, it appears they only do so to apply a patch. Otherwise it is left up all day every day.
The normal TC shard went down about 3pm UK time if I remember correctly, Not sure if HS is any different.
Yeah, this is what I meant, time when server maintenance is performed. I just didn't want it to be while I was in the middle of something.