Data-centric approaches play an increasing role in many scientific domains, but in turn rely increasingly heavily on advanced research support environments for coordinating research activities, providing access to research data, and choreographing complex experiments. Critical time constraints can be seen in several application scenarios e.g., event detection for disaster early warning, runtime execution steering, and failure recovery. Providing support for executing such time critical research applications is still a challenging issue in many current research support environments however. In this paper, we analyse time critical requirements in three key kinds of research support environment—Virtual Research Environments, Research Infrastructures, and e-Infrastructures—and review the current state of the art. An approach for dynamic infrastructure planning is discussed that may help to address some of these requirements. The work is based on requirements collection recently performed in three EU H2020 projects: SWITCH, ENVRIPLUS and VRE4EIC.