Hello skogar,
As there's currently no option to pause the processing, close Metashape and then resume the operation from the same point, I think you may need to try the network processing feature.
In case there's a stable machine in your lab that wouldn't be rebooted randomly, you can run Metashape Pro as a server there (doesn't require license activation) and use the super-computer as a processing node instance. Then, when it comes to the time the machine should be stopped, you just pause the job on the server (via Agisoft Network Monitor), terminate the node and next time you have access to the processing machine, run Metashape as a node on it again and resume the operation on the server.
Note that such approach is applicable to the tasks that support fine level task subdivision only. Although most of the task do that, there are still some exceptions, like point cloud based (sparse/dense) mesh generation, building UV layout, blending texture.
If you cannot rely on the second machine as a server, you can run it on the very same computer as the processing node, but to terminate it properly you should pause the job, stop the node instance, save the batch list from the server (via Network Monitor) to json file and only after that stop the server. And to resume: run the server, load json, re-connect the node and resume the job.
Hope that the description is not very complicated, but feel free to comment, if you have any difficulties following the instruction.
P.S. just out of interest, what is the resolution of the images your are working with?