Hello wmxz, welcome to our community.
Thank you for the detailed report. Have you tried to access the Shake local page via the IP address that your modem/router has assigned to the Shake itself?
You can find it with the app Fing, as illustrated in this post: Please read before posting!
Does the popup “Shake is down” (which is quite strange, I admit) still appear?
Regarding the logs, if you can SSH into the Shake, could you please copy the entire content of the folder /opt/log, zip it, and attach it to your answer? These are all the files I need to get a deeper look into what could be causing this.
Thank you.