Similar experience... not browser specific nor device specific nor internet ISP connection specific.
I have an ISP= VM cabled connection at one location and an ISP= TalkTalk connection somewhere else... and both frequently generate the "SERVER UNREACHABLE" condition when using VM Webmail.
So unlikely to be anything other than an issue with the VM Webmail interface.
As far as I can tell, my IMAP 3rd-party client does not suffer from this issue.
It is def. very disruptive as it happens usually at least once an hour.