After yet more outages and phone calls to helpdesks I finally have my Internet issues sorted out. The helpdesk guy was pretty stumped on what was causing my outages but I managed to convince him that it was due to another computer on their network somewhere competing for my static IP address. Once he had come around to the idea (and talked to his supervisor) I soon had a fresh static IP and a working Internet connection. Throughout this time I was quite thankful I had recently moved my email hosting onto
Google's hosted services. It meant that even though Internet was down for most of the day no mail was lost but it did result in no StressFree website for a while :-(