"I have accounts with two other banks and have never experienced their Apps being down.
"What is going on at BNZ."
Another customer said the bank should change their motto to "Major Outage".
"Switching to ASB next week," one Twitter user threatened.
"Your network problems are too frequent. Couldn't pay for groceries. Embarrasing [sic]."
A social media administrator for the bank said online the team was working to fix the problem and actively monitoring the situation.
A BNZ spokeswoman said customers had been experiencing an intermittent issue which had been sporadic throughout the day. There hadn't been a blanket outage.
BNZ apologised for any inconvenience caused and said crews were continuing to work on the issue tonight.
The spokeswoman advised people who were experiencing problems to try logging out and logging in again after a few minutes.