MyCloud keeps disappearing off network

My Cloud OS 3 Personal & Network Attached Storage My Cloud
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From what you are describing. It looks like the IP address is correct. I say this because when the WD Access stops media streaming still works and twonky works. For these to work the IP address needs to be correct. It looks like the network just stops talking. If running windows one could try to use the network monitor to trace the network traffic of this device. Not sure what the program is called on a mac.
I suspect that something on the device is causing the device to have excessive CPU or something similar. I would suggest that you SS into the device and run sar or ps -eaf logging the output to a file on disk. When the system fails and reboots check the file to see if you can find something.