Performance issues in software-defined network (SDN) controllers can have serious impacts on the performance and availability of networks. In this paper, we consider a special class of SDN vulnerabilities called stateful performance issues (SPIs), where a sequence of initial input messages drives the controller into a state such that its performance degrades pathologically when processing subsequent messages. Uncovering SPNs in large complex software such as the widely used ONOS SDN controller is challenging because of the large state space of input sequences and the complex software architecture of inter-dependent network services. We present SPIDER, a practical fuzzing framework for identifying SPIs in this setting. The key contribution in our work is to leverage the event-driven modular software architecture of the SDN controller to (a) separately target each network service for SPIs and (b) use static analysis to identify all services whose event handlers can affect the state of the target service directly or indirectly. SPIDER implements this novel dependency-aware modular performance fuzzing approach for 157 network services in ONOS and successfully identifies 10 new performance issues. We present an evaluation of SPIDER against prior work, a sensitivity analysis of design decisions, and case studies of two uncovered SPIs.