When is Darksteel Juggernaut's power and toughness determined? Can they change?
I am not a judge, but I believe the following sections from the comprehensive rules cover everything:


  207.2a The card may have a characteristic-defining ability that sets its power and/or toughness according to some stated condition. (See rule 604.3.) Such an ability is worded “[This creature’s] [power or toughness] is equal to . . .” or “[This creature’s] power and toughness are each equal to . . .” This ability functions everywhere, even outside the game. If the ability needs to use a number that can’t be determined, including inside a calculation, use 0 instead of that number.


and


  604.3. Some static abilities are characteristic-defining abilities. A characteristic-defining ability conveys information about an object’s characteristics that would normally be found elsewhere on that object (such as in its mana cost, type line, or power/toughness box). Characteristic-defining abilities function in all zones. They also function outside the game. 


And if you check the card rulings for Serra Avatar (with the same ability), it has the following ruling:


  10/4/2004: Its power and toughness are continuously calculated.


So, its power and toughness are always defined, in all zones, and always updated.  If anything needs to reference its power and toughness, determine what that is.  If a new artifact comes into play, it automatically goes up in power and toughness.