Some TSB customers couldn't access online banking services on Monday.
Users on both the app and the website received error messages when trying to access their accounts.
There are dozens of comments on social media saying affected customers were unable to get past the security questions, some for several hours.
The bank said it was working to fix the issue as quickly as possible, and that only a "very small number" of people were affected.
A number of users reported their accounts had been blocked while trying to log in with the correct details.
Others complained that they could not access support for this issue over the phone or via Twitter.
It was also suggested that the difficulties had started over the weekend.
A TSB spokesman told the BBC:
"We're aware a very small number of customers have been experiencing issues accessing their internet banking.
"We're working to fix this for them as quickly as possible and apologise for any inconvenience caused. Our mobile banking app remains fully functioning."
It is unclear how many customers were affected by this problem but it comes just months after an outage in April affected hundreds of users.
And last year, a "processing error" meant wages and other payments were not paid into some TSB customers' accounts.
In April 2018, a similar IT failure left up to 1.9 million TSB customers unable to bank online for several weeks.
Customers were moved on to a new system, but an investigation found it had not been tested properly before going live. It cost TSB a total of £330m for customer compensation, fraud losses and other expenses.