DH and I are subscribed to a number of migration to NZ sites and we received this in today from "New Life New Zealand" which might explain some of the delays people are facing if medical assessment is required.

A very big issue for many applicants at the moment is the fact that there are simply not enough Medical Assessors at Immigration, and so any medical issues impacting on your application may lead to a long delay on your visa being granted. For example, in the UK at the moment it is taking an extra month for an application to be referred to the Medical Assessor, and then potentially another month each time they ask for further information and it has to go back to them again. In New Zealand it is taking an extra 2-3 months each time, with the Medical Assessors still reviewing medicals that were submitted in December!! You can imagine the impact this might have on your visa application if you have a job offer or course of study waiting! Immigration has just hired 3 additional Medical Assessors and is training them up, but it will take some time for these extreme delays to reduce.
Hopefully those MAs will get trained up fast!