Reports emerged earlier this week that next to no one was watching the station aimed at 25- to 34-year-olds.
Its news programme, called 'The News Show', at one point during the war in Iraq registered zero ratings, according to Barb.
The Barb "zero" means that the station has recorded less than 100,000 viewers in total. In reality, the programme was likely to have had some viewers, but the technology in place does not allow Barb to say exactly how many.
The BBC said the drop was understandable as viewers opted to tune in to rolling news during the Iraqi conflict.
A spokeswoman for the BBC said: "It's very unfair to pick out that one day when most multichannel viewers would have gone to the rolling news networks."
She added: "'The News Show' was maintaining an average of 30,000-40,000 viewers per episode, and had reached more than 90,000."
However, it is not only audience figures for 'The News Show' that have been disappointing. Other programming on the station, which airs a mixture of comedy, new drama and celebrity-orientated shows, have also performed poorly.
In particular, the channel's 20-part documentary series about footballer-turned-actor Vinnie Jones also attracted a zero rating. Some have questioned the rationale behind the decision to devote so much airtime to the ex-footballer and Hollywood bit-part actor.
However, the BBC said that the figures for BBC Three had been reported in isolation and did not take into account that digital viewing had fallen across the board.
"With BBC Three in general, no way are we failing," the spokeswoman said.
The BBC claims that Three's average share of the audience has been 2.1%, which it says is more than double that of BBC Choice, the service it replaced.
"The general average is still 65,000-75,000 viewers," she said.
BBC Three launched on February 9 and last month the corporation hailed the success of the new service with the release of audience figures that show that 2.4m viewers in its target audience of 25- to 34-year-olds had tuned into the channel in its first month on air.
It said the channel has taken an average nightly share of 2.5% of the audience for this age group, ahead of commercial rivals E4, UK Gold, Bravo and Paramount, according to the broadcaster.
Among the programmes the BBC highlighted as successes include 'Burn It', a drama featuring six friends facing up to turning 30 and the responsibilities that come with it, and factual series 'Body Hits' and 'Liquid Assets'.
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