BBC News has seen dozens of complaints about screen flickers affecting the Amazon Echo Spot and Amazon's response.
One owner, in Hampshire, said his device had started to flicker 16 months after he had bought it.
He was told its one-year warranty had run out and offered 15% off a new one rather than a refund or repair.
Under EU law consumers must be given a minimum two-year guarantee "as a protection against faulty good or goods that don't look or work as advertised".
A thread on Amazon's help forum about the screen problem, which dates back several months, has had nearly 20,000 views and there are many tweets about the issue.
A poster on the same topic on Reddit said it appeared to be "a widespread problem".
"One-year warranty, and I, like many, are right outside it," another, in the US, said.
An Amazon representative told BBC News: "We are investigating. If customers have any questions or concerns, they should contact customer service."
The Echo Spot retails at £119.99 on the Amazon website.
Overall it has received good reviews, with the website TrustedReviews awarding it 4.5 stars.
What Hi-Fi describes it as "an impressive piece of kit" and notes "the display is sharp".
In the UK, goods are covered by the Consumer Rights Act 2015 (CRA), as well as European Union law.
"Generally we would always advise consumers who have goods which are clearly faulty to go back to the retailer in the first instance to make their claim under the statutory rights which exist under the CRA," Sylvia Rook, lead officer for fair trading from the Chartered Trading Standards Institute, said.
"Consumers have up to six years to make a claim for faulty goods (five years in Scotland).
"That doesn't mean that goods have to last for six years but it does mean that a trader can't refuse to consider a claim just because the consumer has had an item for a period of time, if it is proved to be faulty."