Design of robust supervisory controllers for manufacturing systems with unreliable resources has received significant attention recently. Robustness analysis provides an alternative way to analyse a perturbed system to quickly respond to resource failures. Although we have analysed the robustness properties of several subclasses of ordinary Petri nets (PNs), analysis for non-ordinary PNs has not been done. Non-ordinary PNs have weighted arcs and have the advantage to compactly model operations requiring multiple parts or resources. In this article, we consider a class of flexible assembly/disassembly manufacturing systems and propose a non-ordinary flexible assembly/disassembly Petri net (NFADPN) model for this class of systems. As the class of flexible assembly/disassembly manufacturing systems can be regarded as the integration and interactions of a set of assembly/disassembly subprocesses, a bottom-up approach is adopted in this article to construct the NFADPN models. Due to the routing flexibility in NFADPN, there may exist different ways to accomplish the tasks. To characterise different ways to accomplish the tasks, we propose the concept of completely connected subprocesses. As long as there exists a set of completely connected subprocesses for certain type of products, the production of that type of products can still be maintained without requiring the whole NFADPN to be live. To take advantage of the alternative routes without enforcing liveness for the whole system, we generalise the concept of persistent production proposed to NFADPN. We propose a condition for persistent production based on the concept of completely connected subprocesses. We extend robustness analysis to NFADPN by exploiting its structure. We identify several patterns of resource failures and characterise the conditions to maintain operation in the presence of resource failures.