Digital twins (DTs) represent a key technology in the development, real-time monitoring and optimisation of cyber–physical systems (CPSs). Such potential emerges as a result of the real-time coupling between DTs and their physical counterparts, where it is possible to make use of operational data as it is being generated in order to aid decision-making. Harnessing this potential presents several design challenges, such as the parallel operation of the DT and its physical twin (PT), and the necessary synchronisation thereof, to ensure coherent execution of the system in ensemble. In this paper we present an approach that handles situations where a DT and its PT get out of sync as a result of disturbances in the normal operational conditions of the DT–PT system, e.g., due to network degradation or temporary network drop. The purpose is to provide a best-effort functionality covering: user notification, degradation of DT to digital shadow (DS), with recovery mechanisms to re-establish the synchronisation between DT and PT.