The BBC host hit back at SNP’s leader in Westminster after he defended the decision to push the vote back to 2019.
Coburn hinted support was waining for the party and independence, as she grilled the Scot on their manifesto release.
Ms Sturgeon, who is bidding to recapture 56 of the 59 Scottish seats won in the 2015 General Election, set out the party’s new referendum timetable and its “anti-austerity” plans.
Discussing the document launch on the BBC’s Daily Politics, Mr Robertson said: “Nothing has changed, we’ve said we’re favour of the people having a choice about their future when we have clarity and the outcome of the Brexit negotiations.
Jo Coburn insisted independence support is waining in attack on SNP's Angus Robertson
Support for a second independence referendum just isn’t moving in your favour
“I think it is sometimes lost in the debate, at the end of the negotiations there is supposed to be a period for the approval or rejection of that deal.
“All 27 other EU member states will have a say in our future, as well as the European Parliament, in those circumstances we feel that is the appropriate time.
“If it is right for everybody else to have a say and consideration in our future, we think we should have that right as well.”
However, Coburn leapt back in attack accusing the SNP of a “massive climbdown”, after they were so persistent on calling for Scottish independence in the wake of Brexit.
She said: “Isn’t it a massive climbdown to change the timing of when you are now demanding to have that second referendum?
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“Actually, in Nicola Sturgeon’s speech, there was barely any mention of it. It seems to have disappeared at all, is that to do with the fact that the dial in terms of support for a second independence referendum just isn’t moving in your favour?”
Mr Robertson responded by suggesting “now is not the time” to hold such a vote, claiming Ms Sturgeon and Theresa May “are at one on that issue”.
He added: “What is important is people have clarity… people understand what the outcomes of the Brexit negotiations are likely to be.
“Increasingly, people are right to fear – regardless if they voted for Leave or Remain – that we are heading towards the hardest, most damaging form of Brexit.
Nicola Sturgeon's comical moments on the campaign trail Mon, May 22, 2017 PA 1 of 13
SNP leader Nicola Sturgeon stops for an ice cream after making an election campaign visit to Scottish Gas HQ in Granton, Edinburgh
“In those circumstances, it would be absolutely right, and not least, of course, because we’ve already had an election on that in Scotland where the party that had a manifesto commitment to holding a referendum on the outcome after Brexit negotiations was the SNP.”
Speaking at the manifesto launch in Perth, Scotland, Ms Sturgeon demanded the opportunity for Scots to be able to decide on their own future.
She added: “There is too much at stake for Brexit simply to be imposed on Scotland, no matter how damaging it turns out to be.
“Out future must be decided by us, not for us.”