If it seems that the Hub is dropping offline in AnywhereUSB Manager pretty regularly at the 3 week mark, have you checked for processes within that VM instance which run on a 3 week schedule?
Reason I ask is because I was working with a customer describing a similar issue, but in his case, a connected USB device was basically being "Ejected" once per week. Turns out, the "once per week" timing for when the USB device disconnection was occurring lined up perfectly with when they ran a backup of the Virtual Machines. He was somehow able to "ignore" or skip the USB device when the VM backup was run, and wouldn't you know it, the problem disappeared.
I just wanted to mention the above due to the similarity of the event you're describing, but also to point out that the AnywhereUSB Manager client-to-Hub relationship is also vulnerable to outside forces at times, especially when that AnywhereUSB Manager client is running on an instance running on top of a Virtual Machine.
Hope that helps!