It's perfectly valid to say there shouldn't be another referendum for a long time, if ever. Its not undemocratic either as the vast majority of countries prohibits secession.
And, no, the devolved administration in Scotland cannot have a yearly referendum either. Not only would it be hugely destabilising, but it is definitely ultra vires (beyond the power)!
You make the classic mistake in thinking that just because the SNP get more votes than any single party that means a majority of the electorate are in favour of independence.
"A vote for the SNP is not a vote for another referendum." - Nicola Sturgeon
That statement was valid then and is still valid now. People are voting for the SNP to run Scotland within the UK is the very least that can be said about their voters.
Voluntary union?
The UK is a UNITARY SOVEREIGN STATE! International law is very, very clear as the Canadian Supreme Court ruling shows:
"It is clear that international law does not specifically grant component parts of sovereign states the legal right to secede unilaterally from their "parent" state....
The various international documents that support the existence of a people's right to self-determination also contain parallel statements supportive of the conclusion that the exercise of such a right must be sufficiently limited to prevent threats to an existing state's territorial integrity or the stability of relations between sovereign states...
A state whose government represents the whole of the people or peoples resident within its territory, on a basis of equality and without discrimination, and respects the principles of self-determination in its own internal arrangements, is entitled to the protection under international law of its territorial integrity."
- Canadian Supreme Court ruling on the issue of secession
Ininternational AND domestic law, territorial integrity takes precedence. Regions of unitary sovereign states can only hold a referendum with the consent of the Sovereign Government. Ergo, can only leave on that basis. But there is no obligation for any unitary sovereign state to agree to any referendum and, therefore, agree to secession in the first place!
As for social problems, these have progressively got worse the longer the SNP has been in power. Its worse under the SNP than it was under the devolved Labour administration in Scotland or during the period of direct rule. Indeed, Northern Ireland and Wales do NOT have Scotland's rate of drug deaths under the SNP. Northern Ireland's educational ranking in PISA has been higher than Scotland under the SNP too. And so on. None of these can be wholly blamed on the UK since the SNP has complete responsibility for all devolved issues in Scotland. If that flawed logic applied, why have other parts done better in various areas within the same union?
But Nationalism requires all blame to be laid at the door of the Sovereign Government. And so the SNP drive that feeling. An Irish Nationalist leader John Hume asserted that a "hallmark of fascism" is that "the Brits are to blame for everything!". His point was political actors in Northern Ireland were very much to blame since they were divided. The same applies in Scotland where the SNP has successfully Ulsterised Scottish politics.....
The union cannot be blamed for everything.