I just found this tweet by Anonymous.
#Anonymous Do NOT DDOS http://JW.org we need DATA DUMP First. #Watchtower #OpPedoChat
It looks like they want the site to be up at the moment so they can gather information. I don't know how it all works, but I know they are gathering a bunch of emails and other data. Taking down the site for a little while probably isn't very difficult, but they want to actually hack the site so it displays a message from them.
This makes me think that the earlier disruptions may have been from maintanence.