As industrial Internet of things (IIoT) for Manufacturing Service Collaboration (MSC) is becoming the current trend to accelerate the upgrade iteration of manufacturing capability, developing the robust IIoT platform operation mechanism for MSC is crucial to promote the continuous and stable service collaboration in the presence of supply and demand uncertainties. This paper studies the operational robustness of the IIoT platform for MSC. Firstly, the operation performances, requirements, and challenges of the IIoT platform towards manufacturing collaboration are analysed in classified platform practices, which can provide a comprehensive cognition about platform operation for manufacturing collaboration. Then, to evaluate the tolerance and persistence capabilities of MSC under supply and demand uncertainties, a graph-based operational robustness analysis method of the IIoT platform for MSC is proposed. The IIoT platform operation network for MSC is modelled as an interdependent network-of-network structure based on graph theory, which helps to characterise MSC performance properties under complexities. By combining manufacturing properties with network statistics, the evaluation metrics of operational robustness are established, which is done to quantise the MSC effectiveness under uncertainty effects. A case about customised manufacturing of automobiles illustrates the application of the proposed methods. Finally, future studies about robust MSC regulation are discussed.