Scaling the size of assembled neutral-atom arrays trapped in optical lattices or optical tweezers is an enabling step for a number of applications ranging from quantum simulations to quantum metrology. However, preparation times increase with system size and constitute a severe bottleneck in the bottom-up assembly of large ordered arrays from stochastically loaded optical traps. Here we demonstrate a method to circumvent this bottleneck by recycling atoms from one experimental run to the next, while continuously reloading and adding atoms to the array. Using this approach, we achieve densely packed arrays with more than 1000 atoms stored in an optical lattice, continuously refilled with a 3.5 s cycle time and about 130 atoms reloaded during each cycle. Furthermore, we show that we can continuously maintain such large arrays by simply reloading atoms that are lost from one cycle to the next. Our approach paves the way towards quantum science with large ordered atomic arrays containing thousands of atoms in continuous operation. Published by the American Physical Society 2024