The bank's internet banking and mobile app were inaccessible to some customers this morning.
There have been a series of outages over the past month, amid spate of cyber attacks on major New Zealand websites.
One customer posted on the bank's Facebook page that she had "no patience left for this".
"Your service is no longer reliable and we are very much over this. You have definitely lost me as a customer just as soon as i can i am changing banks."
Another woman said the outages were happening too often.
"Being able to access my own money should be easy & available!"
One customer asked if the bank would be paying their late fees for not being able to make payments on time.
"Hey Kiwibank...are you going to pay for my late fees and interest charged by other companies because I can't my bills for what seems like the 4th time this month???
"How can we trust you with our money while you can't even operate a simple online banking forum which every other bank seems to be able to do."
Some just wanted an explanation for the cause of the ongoing problems.
"Can we have an explanation for these issues? It's been happening too often for too long by now."
In a post to Twitter Kiwibank said it was aware some customers were having challenges accessing its mobile app and Internet Banking this morning.
"We're currently looking into this. Thanks for your patience and we'll keep you updated."
But that patience is wearing thin with customers with one customer telling the bank to stop asking for patience.
"Make it stop! Start telling us how you are going to make it up to us, compensation for embarrassing us when out shopping or being late with bills... and fix this problem for good!"
Kiwibank isn't the only organisation to have been hit by IT problems recently.
Earlier in September, cyber attacks took Kiwibank, ANZ, NZ Post and MetService offline.
Cert NZ confirmed at the time it was aware of a DDoS (Distributed Denial of Service) targeting a number of New Zealand organisations.
It is unclear at this stage if the latest issues facing Kiwibank are again related to DDoS attack.
