More than 20 per cent of all calls were abandoned in May, rising to 32 per cent for the past two weeks of the month.
On May 24, June 5 and June 7, over half of all calls were abandoned. On May 24, those calling to register for a vaccine faced an average wait of more than 23 minutes.
Scottish Labour said the figures raised concerns about whether the helpline had the resources it needed.
Deputy leader and health spokesperson Jackie Baillie said: “It is deeply worrying that thousands of Scots who are seeking help or guidance on the vaccine programme are being left hanging on the telephone or having to give up without answers.
“We simply cannot have thousands going without the help and guidance that they need.
“It is the duty of the Scottish Government to ensure that the vaccine helpline is fit for purpose and that staff are properly supported in carrying out their duties.”
The concerns come as Scottish Labour also renewed calls for the gap between vaccine doses to be cut to six weeks, following the example of Northern Ireland.
Ms Baillie said: “This proves that we can speed up vaccination when needed – the SNP are simply choosing not to act.
“The evidence is piling up by the day on how effective double vaccination is against the Delta variant, but we are still dragging our feet – and against the recommendations of the WHO [World Health Organisation] at that.
“The science is there and so are the vaccine stocks – all that is missing is the political will.”
Nicola Sturgeon has called previous demands from Labour to cut the dose gap “irresponsible”, and not in line with JCVI guidance.
A spokesperson said the Scottish Government will follow JCVI advice.
“We note comments from JCVI adviser Professor Anthony Harnden who underlines that real data vaccine effectiveness studies show a lower vaccine efficacy with shorter intervals and that modelling suggests the number of infections could actually rise,” they said.