I just saw the LiveGrid alert pop up again, and so decided to try pinging all the listed umXX.eset.com hostnames and the avcloud.e5.sk hostname.
I was getting successful ping returns from the avcloud.e5.sk and the umxx.eset.com hostnames up until um14.eset.com, where upon it timed out a couple of times and then resolved on the 3rd attempt. As soon as it resolved the warning disappeared. Note that I was also using a remote VPN to connect to the company domain at the time.