The first test balloon from Wanaka, in 2015, remained in the stratosphere for 32 days, five hours and 51 minutes, before developing a leak and being brought down in Australia.
That record for a mid-latitude balloon flight looks likely to be broken at the weekend.
The longest flight by one of Nasa's high-pressure balloons was 54 days, following a launch in the Antarctic in 2009.
Nasa spokesman Jeremy Eggers said yesterday the organisation was learning a lot from the current flight about providing "assured access to the near-space environment for low-cost scientific investigations and technology demonstration flights''.
The balloon is now over the Pacific, off the coast of South America, having completed one orbit of the Antarctic.
The red track in the graphic shows the balloon's current revolution.
Nasa's goal is for the helium-filled balloon to continue flying for 100 days.
It is carrying a Cosi telescope designed to probe the origins of galactic positrons, and study the creation of new elements in the galaxy, gamma-ray bursts and black holes.
