The challenge of persistent appearance-based navigation and mapping is to develop an autonomous robotic vision system that can simultaneously localize, map and navigate over the lifetime of the robot. However, the computation time and memory requirements of current appearance-based methods typically scale not only with the size of the environment but also with the operation time of the platform; also, repeated revisits to locations will develop multiple competing representations which reduce recall performance. In this paper we present a solution to the persistent localization, mapping and global path planning problem in the context of a delivery robot in an office environment over a one-week period. Using a graphical appearance-based SLAM algorithm, CAT-Graph, we demonstrate constant time and memory loop closure detection with minimal degradation during repeated revisits to locations, along with topological path planning that improves over time without using a global metric representation. We compare the localization performance of CAT-Graph to openFABMAP, an appearance-only SLAM algorithm, and the path planning performance to occupancy-grid based metric SLAM. We discuss the limitations of the algorithm with regard to environment change over time and illustrate how the topological graph representation can be coupled with local movement behaviors for persistent autonomous robot navigation.