The literature on monitoring of cross-organizational processes, executed within business networks, considers monitoring only in the network formation phase, since network establishment determines what can be monitored during process execution. In particular, the impact of evolution in such networks on monitoring is not considered. When a business network evolves, e.g. contracts are introduced, updated, or dropped, or actors join or leave the network, the monitoring requirements of the network actors change as well. As a result, the monitorability of processes in the network may be disrupted. This paper proposes a framework to solve the problem of preserving the monitorability of processes in an evolving business network. We first propose a formal model of business networks, contracts, and monitoring requirements. Then, we model network evolution and the mechanisms to preserve the monitorability of the processes in the network for different types of evolution. In particular, the preservation of monitorability requires the actors in the network to take appropriate actions in case of dependencies between already established contracts, and update their monitoring infrastructure to satisfy the new monitoring requirements introduced by evolution. We also define a set of metrics that can be used for supporting decisions regarding the potential evolution of a business network. A case study in healthcare and the discussion of a prototype implementation show the applicability of our framework in real-world scenarios.