Why Sage cloud worksheets freezes or stop working (after some ten minutes) if you don't click on it?

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Under a free plan, a CoCalc project times out after 30 minutes of user inactivity. Interacting with the project within that time keeps it running.

Besides, projects run on machines that can be restarted once per day (which can explain occasional interruption before the 30 min timeout). When this happens, the project gets moved to a different machine in order to resume activity faster (don't wait for the machine it was on to restart). With bad luck, the new machine could have its daily restart a little bit later and cause another shorter timeout; not sure if that happens a lot.

The pricing page lists plans to get "member hosting" and longer timeout. https://cocalc.com/policies/pricing.html

There is also a Docker container for CoCalc which lets you run an instance of CoCalc on your computer. I guess projects running there do not time out. You would need to check if the features you care about are present on that version of CoCalc (for instance it has less Jupyter kernels, but you could also modify the docker script to install additional ones). It certainly has CoCalc Sage worksheets (.sagews).