Smile Bank customers have been unable to access their online banking accounts for five days in a row.
The online-only bank, owned by Co-Operative Bank, said it was working urgently to resolve the problem.
But the latest service outage proved to be the "last straw" for longtime customer Emma Hopkinson-Spark.
After 16 years, she left Smile Bank on Friday after she was unable to view a crucial re-mortgage payment.
"I'm really disappointed in Smile Bank," Ms Hopkinson-Spark, chief of staff at a tech consultancy business in Weston-super-Mare, told the BBC. "The outages this week were the tipping point."
Ms Hopkinson-Spark said she had not been able to access her online banking account for several days. Although she can still withdraw money from cash machines and pay for items using her debit card, she cannot send payments or view her payments.
"Yesterday my husband rang me in a flap saying he was trying to pay for groceries and didn't have money in his account," she said. "He needed me to transfer money to his account and I couldn't."
Her frustration came to a head when her mortgage firm said they had sent a payment of almost £100,000 to her current account, but she could not see it there or do anything with the funds.
She decided to close her current account, cash ISA and savings account with the bank and is transferring her funds to a different bank.
Smile Bank, which has around 100,000 customers, has apologised for problems with its online banking and mobile app, but it was unable to provide the BBC with a reason for the outage, or say when the problem would be fixed.
Image copyright Smile Bank Image caption Customers have complained that Smile Bank is not communicating with them about the outages"We're sorry that our Smile customers have been unable to use our mobile app and online banking as they would usually in recent days," the company said in a statement.
"We are working hard to restore their access as soon as possible and we apologise for any inconvenience caused.
"Customers can use their cards and make transactions as normal and if they need support with their account they can call our customer service team."
'We're getting really panicked'
Vicky Wevell, a self-employed editor in Nailsea, near Bristol who has been with the bank for 20 years, said Smile Bank's mobile app had gone downhill in recent years, with outages for hours at a time.
Like other Smile Bank customers who spoke to the BBC, she said a lack of communication during the recent issues had made her worried about the safety of her funds.
"I'm really angry actually and have been getting progressively angrier this week," she said. "It's less to do with the outage and more to do with their communication."
She said she was also on the verge of switching banks, because she could not see which invoices for work done had been paid by her clients.
"How are we supposed to do any business?" she said. "[We're] getting really panicked, is our money secure?"
Making enquiries
Jackie Smart, an office administrator in Aylesbury, said it took days for the bank to put a notice up about the outage on its website and communication remains difficult.
Image copyright Getty Images"I'm feeling frustrated and worried because I don't know what's happening. You can get through on the automated service to hear your balance when you ring through, but it's actually waiting to speak to somebody that takes a long time," she said.
Set up in 1999, Smile Bank was one of the earliest online-only banks. Its parent company, Co-Operative Bank, is owned by a number of hedge funds, which last year were reportedly exploring a sale of the business.
The BBC understands that the outage is caused by an issue that is only affecting Smile Bank's platforms, but not other brands owned by Co-Operative Bank.
Smile Bank customers have been advised to call the bank if they require assistance with their accounts on 03457 212212 during opening times, which are: Monday-Friday 08:00-18:00 BST, and on weekends between 09:00-17:00 BST.
As call waiting times may vary, the bank told the BBC that customers can also to contact Smile Bank's Twitter and Facebook accounts to make queries.