The YouGov survey for the Times on the future of Kezia Dugdale’s party found just 34 per cent thought it was here to stay and would remain important over the next 10 years.
A higher proportion of respondents (36 per cent) said Scottish Labour was finished and would not be a force within a decade while the remainder did not know.
The research was conducted in the days before the Holyrood election on May 5, in which Labour was beaten into third place by Ruth Davidson’s Scottish Conservatives, finishing on 24 and 31 seats respectively.
Respondents judged Labour to have pursued a negative campaign in the run-up to the vote, with an aggregate score of -16 compared to -13 for the Tories and +22 for the SNP.
However, when asked about how honest or dishonest the campaigns were, Labour fared better on -2, with the Tories thought to be less honest on -7. The SNP scored +12.
In advance of the vote, a third (33 per cent) thought Ms Dugdale should stay on as leader in the event her party finished in third place while 32 per cent said she should go.
A spokesman for Scottish Labour said: “This was always going to be a tough election for Labour, coming so soon after last year’s general election result.
“We ran an honest campaign that said if we want to stop the cuts to schools and the NHS then those at the top would have to bear the greatest burden.
“As the largest centre-left party in Holyrood, we will continue to make the case for using the powers of the Scottish Parliament to stop the cuts and invest in the future of our economy.”
YouGov polled 1,445 adults in Scotland between May 2 and 4.