Once an AnywhereUSB is connected to a host computer and installed properly, it should automatically attempt to re-connect if the host computer is ever rebooted.
If this does not seem to be happening, to troubleshoot this issue, reboot the host computer (re-create the issue) then note the "Connection Status" at the top-right of the AnywhereUSB Configuration Utility.
If the Status is "Connected to (IP address)" then the AnywhereUSB is already connected to a different host computer - whatever that IP address corresponds to. Likely, there are two computers that are both configured to connect to the same AnywhereUSB (or the same Group, in the case of a Multi-Host capable AnywhereUSB being used), essentially "fighting each other" for the connection. If this is indeed the case, the second computer "steals the connection" while the other computer is rebooting.
Because multiple host computers cannot be connected to the same AnywhereUSB at the same time (or the same Group at the same time, for MHC-capable AnywhereUSBs, you will need to forcibly prevent the other conflicting computer from attempting to connect. To do this, click Edit / Connection List in the AnywhereUSB Configuration Utility, and delete the entry for the AnywhereUSB in question.
If the Status is "Connecting to this host PC..." then review this article.