It displayed an error message on some computers, but not others, saying access had been blocked because of a "high volume of visitors".
Users had complained that this was inaccurate bearing in mind it was being shown in the early hours of the morning and the issue was continuing.
Argos said it was an intermittent problem that might take time to solve.
The company - which is owned by the Milton Keynes-based Home Retail Group - said that its site was currently working, but might face further issues.
"Following planned maintenance to our website and apps, we have been experiencing some technical issues which means customers may have limited access to our website at intermittent periods," a spokeswoman told the BBC.
"We are really sorry for any inconvenience caused. Serving customers is our absolute priority and are pulling out all of the stops to fix the problem as soon as possible."
She said the site had only been offline to all customers for "just over half a day" on Tuesday morning.
The firm had used social media to apologise for the problem, but unless customers searched for the posts they would not have been aware of them since more recent marketing tweets were embedded into the "fault" page.
The spokeswoman said the failure to properly explain the problem on the page was in itself "caused by a technical issue which is currently being fixed".
One retail expert said it was not unusual for website updates to create glitches, but suggested the company should have explained the issue more clearly.
"Any retailer that has a robust enough e-commerce platform should have some sort of contingency plan in place around communication," said Steve Mader, from the consultancy Kantar Retail.
"Argos has historically done a fairly good job of doing iterative improvements on its website - although in heavy periods leading up to Christmas it has been known to slow down or restrict access.
"I think for every retailer, having an outage like this can be a wake-up call."
Retailer Argos's website has suffered problems for a second day following a revamped design of the site.