MikeB4: If you think it's bad here, the Branches we supported on the west coast South Island had terrible electricity supplies. Our Servers would go down at least weekly if not more especially Westport and Greymouth. I doubt if a day would go by with me receiving alerts for Server not contactable which invariably would be a power outage. They featured as peaks on each and every monthly report I sent upstairs.
WestPower (the West Coast lines company) have a distribution area as long as the distance from Auckland to Wellington, but extremely thin with almost no opportunities for parallel distribution lines to provide redundancy. Also somewhat fewer (and poorer) people than Wellington, let alone Auckland, Wellington and all the places in between, to pay for construction and maintenance of such an improved network.
If you run a branch network on the West Coast, one of the costs of continuing to do business there would be providing robust UPS solutions - including gensets.
I'd guess the problems in J'ville are most likely caused by clashing spans on the high-voltage (33KV / 66KV?) reticulation from the Transpower Grid Exit Point to the local distribution substation. Undergrounding 33KV or 66KV is very, very expensive and would be a real challenge in the hilly parts of Wellington where an overhead line can jump a gully that would be an engineering nightmare to route around or through.
And since Wellington Electricity (not "WEL", that's Waikato) is IIRC owned by a Hong Kong Chinese investment company, and are like all lines companies strictly regulated as to the profits they can earn, the chances of them stumping up the cash to underground these lines is probably mathematically indistinguishable from zero.
Move house?