If the trenches of WW1 were a long continuous line, when a sector was captured in battle why didn't the victors just move all the way down the line until the whole line was captured?
^ These answers I've give previously should be pertinent
If the trenches of WW1 were a long continuous line
In theory, yes, in practice, no. Trenches in their shape and construction varied from sector to sector based on the units that held them, the terrain and makeup/layout of the ground, and other typically geological factors such as soil content and water table height. Further more, in the case of the German defenders, the Western Front by summer 1916 consisted of no less than three positions, each comprising at least 3 to 4 lines of trenches connected by communications trenches. By 1916, notably in the Battle of the Somme, the Germans were responding to attempts to 'roll-up' their lines in the way you describe by establishing 'Switch Lines' either digging them or creating them from the communications trenches, to 'fence in' any penetration of a position.