21 shows recorded no audience some days, according to the Mail on Sunday.
The viewing figures prompted media watchers to brand the channel a waste of taxpayer money.
But a BBC spokesperson said: "It's not unusual for digital channels outwith the main five to occasionally record zero audiences."
According to the Sunday newspaper report, on one particularly quiet day last month the new channel had an average audience of only 7,200 people.
The figures were gathered from The British Audiences Research Board (Barb) between February 24 and June 2 this year. Barb provides data from meters fitted to TV, computers and tablets from 5,300 panel members.
Among the 21 shows to record no viewers at all were several editions of news bulletin The Seven, discussion show The Collective and new music programme Tune.
Former BBC editor Tim Luckhurst, who is now a professor in journalism, said: "These figures are deplorable. But they simply confirm the central flaw in the entire project - there was never a shred of audience demand for it.
"It was launched as a forlorn attempt to please the SNP, a classic example of why the BBC should never bow to political bullying."
Scottish Conservative culture spokesman Rachael Hamilton said: "These viewing figures are undoubtedly disappointing. If they remain this low, licence fee payers will ask why so much money is spent on it."
But a spokesperson for the BBC said: "It's not unusual for digital channels outwith the main five to occasionally record zero audiences under the Barb system. There were only 21 instances during core hours when zero audiences were recorded over February 24 and June 2 - seven were just one-minute editions of The Seven just as the channel comes to air.
"Overall, the channel is bucking the trend when it comes to engaging younger audiences."