Reuters / Russell Cheyne
The slump in support has defied the expectations of many politicians who speculated that a vote for Brexit would spell the end of the UK.
Some, including ex-PM David Cameron, argued that a Leave vote would cause a surge in support for independence north of the border, where the majority of people voted to remain in the EU.
Cameron said there was a "deeply patriotic" case for voting to remain in the EU because leaving would strengthen the ruling Scottish National Party's argument that Scotland's interests would be better served out of the union.
First Minister Nicola Sturgeon is now pushing for a second referendum, on the basis that Brexit will inevitably bolster the "Yes" vote - but polls are moving in the opposite direction. So what's happening?
Professor John Curtice is one of the country's leading pollsters and a professor of
"Before the June referendum, around 90% of people said they would vote the same way in a second independence referendum as they did in the first," Curtice said. "That figure is now much closer to 80%."
That "churn" is moving in both directions and appears to be favouring the "No" side.
"The problem for the pro-independence side is that somewhere between a quarter and a third of people who voted Yes in September 2014 voted Leave in June 2016," Curtice said.
"While some people might have switched from No to Yes in the wake of Brexit, as the SNP anticipated, there was also a risk that some people would switch from Yes to No - for them, the prospect of being in a UK outside the EU becomes much more attractive than a Scotland intent on remaining inside the EU," he said.
In other words, a significant number of Yes and Leave voters are deciding it's more important to be outside the EU than it is to be part of an independent Scotland. The poll shows that 36% of Leave voters said they would vote Yes in August but the latest poll shows that figure has fallen to 29%.
"Brexit certainly hasn't proven to be advantageous for the "Yes" side," Curtice said. "Sturgeon's apparent assumption was that Brexit would shape the apples off the tree in her direction. In fact, some of the apples have gone in the other direction."