Out of disk space
Screencastify needs more than 1 GB of free local disk space to work properly - even if you store your recordings on Google Drive. This is because the upload to Google Drive happens after the recording has been completed. So it still needs some local disk space temporarily.
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If you don't have a way to free up more local disk space on your device, you force Screencastify continue recording anyway, by disabling "Pause on low disk space" in the Screencastify Options. This is not recommended in general, but may work well enough for short recordings.
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