Your enemy is the waste heat.
In space, you have exactly one method available to get rid of heat, and that is to radiate it away. All big spacecraft like the space shuttle and the ISS must include radiators to avoid overheating.
Generation ships have a power consumption that's roughly linear to the amount of people on board, and people on board grow with the volume of the ship ($\approx x^3$). The available surface area for waste heat radiation, however, only grows with the surface of the ship ($\approx x^2$). So, as you scale your generation ships up, you will run out of surface area for heat radiation eventually.
Now, you could say: Oh, well, then I just build huge radiators that reach out far into space. This will work for a while, but eventually you get the problem that you need to transport the waste heat from the core of the ship all the way to the tips of the heat radiators. The longer this trip becomes the less efficient the cooling will be (more energy is expended on pumping, and it becomes harder to isolate the return pipes sufficiently from the environment as they go down into the heart of the ship).
However, you can still build a huge ship that both has enough radiative surface and can withstand destruction of its parts (= the redundancy advantage of a fleet of ships):
Your ship is basically designed as a gigantic space station. It's assembled from modules and hubs that are connected via some standard connector system. Each module is basically a long tube that has its own heat radiators attached, and is connected to one hub at each end. The hubs are designed so that they mate to six modules in a single plane, and to three modules diagonally upwards. Thus one half of the nodes form a single layer of triangles with 2/5 of the modules, the other half of hubs form a second layer with another 2/5 of the modules. These two layers are connected by the last 1/5 of the modules, using the diagonal upwards connections of the hub. This forms many more triangles which are not parallel to the two planes, and thus provide lateral stiffness to the ship.
As you may know, triangular constructions are extremely stiff and never produce any bending forces on the individual beams. That's why you see such triangular construction at each and every construction crane.
You grow this ship simply by adding modules to the edge of the double plane. As such, the effective surface of the ship grows linearly with its usable volume. The mating mechanism between modules and hubs havehas air locks, valves on all pipes, and electrical switches on all power lines that pass through themit. This allows defective modules/hubs to be separated from the ship in any manner that might be necessary. An open connection, however, allows free exchange of whatever the different modules want/need to exchange, allowing the ship to act like a big city.