Maintaining inter-actor connectivity is extremely crucial in mission-critical applications of Wireless Sensor and Actor Networks (WSANs), as actors have to quickly plan optimal coordinated responses to detected events. Failure of a critical actor partitions the inter-actor network into disjoint segments besides leaving a coverage hole, and thus hinders the network operation. This paper presents a Partitioning detection and Connectivity Restoration (PCR) algorithm to tolerate critical actor failure. As part of pre-failure planning, PCR determines critical/non-critical actors based on localized information and designates each critical node with an appropriate backup (preferably non-critical). The pre-designated backup detects the failure of its primary actor and initiates a post-failure recovery process that may involve coordinated multi-actor relocation. To prove the correctness, we construct a formal specification of PCR using Z notation. We model WSAN topology as a dynamic graph and transform PCR to corresponding formal specification using Z notation. Formal specification is analyzed and validated using the Z Eves tool. Moreover, we simulate the specification to quantitatively analyze the efficiency of PCR. Simulation results confirm the effectiveness of PCR and the results shown that it outperforms contemporary schemes found in the literature.