People considered to have ignored safety advice before losing money in online banking scams could soon be denied compensation by banks.
About 2,000 Britons have been victims of 'phishing' scams
The Association for Payment Clearing Services (Apacs) said a "safety net" existed while banks were still making customers aware of online fraud risks.
Banks have refunded £4.5m to about 2,000 victims of online banking scams.
But Apacs said that in some years' time compensation could be denied if people had safety information but ignored it.
Apacs director of corporate communications Sandra Quinn said there had been an increase in so-called "phishing" scams in recent months.
"Phishing" usually takes the form of an e-mail purporting to be from the person's bank seeking account information, often linking to a bogus website.
Miss Quinn said: "We want to make sure customers know what types of frauds there are and how to avoid being a victim.
"While customers don't know of all the risks, the safety net exists."
But she added: "What we have always said is that we won't forever provide a guarantee.
"A good parallel might be with something like card fraud - if you act reasonably, you are covered."
She said the majority of victims would fall within this category.
But where a customer had "not acted with care and been negligent", banks in three or four years' time could begin refusing refunds, Miss Quinn said.
"Perhaps the customer has been a victim once, gets told all the information, then falls victim again - we have known that to happen."
Banks have urged customers never to respond to unsolicited e-mails supposedly sent by them, and never to reveal pin codes or passwords.
Apacs, which co-ordinates banks' anti-fraud efforts, has launched a website - Bank Safe Online - offering advice.