We investigate the emergence and persistence of modular structure or communities through of a mechanism of adaptive rewiring in coevolutionary networks. We characterize the topological structures arising in a coevolutionary network subject to an adaptive rewiring process and a node dynamics given by a simple voter-like rule. We find that, for some values of the parameters describing the adaptive rewiring process, a modularity structure emerges on a connected network. We show that the emergence of communities is associated to a decrease in the number of active links in the system, i.e. links that connect two nodes in different states. The lifetime of the community structure state scales exponentially with the size of the system. Additionally, we find that a small noise in the node dynamics can sustain a diversity of states and a community structure in time in a finite size system. Thus, large system size and/or local noise can explain the persistence of communities and diversity in many real systems