It unravels in the fifties or sixties. Maybe the seventies. Too many people, too few jobs.
The massive lack of working age males (25-49) probably contributed a lot to the USSR's decline, in 1950 the RSFR only had 62 men aged 25-49 per 100 women in the same age bracket. In the same way that interwar France's elite was stand-ins for men who had died in the trenches, there are loads of inventions and solutions to various problems that were never created in France. France lost a lot of self-confidence during the "hollow years" and Russia may have faced a similar situation below the facade of a confident vanguard party in the postwar period.
All the enterprising young people, especially young men who might've brought something new to Soviet politics or pushed for greater changes and reforms had been killed in the the wars and famines. All that was a left by the '50s was an aging clique of sycophants who had survived Stalin's purges. The economy would've benefited enormously from more workers around.
The stagnation in the '70s onwards was largely a result of people born in the USSR taking over the reins, before then the USSR could burn through the accumulated human capital of the pre-1917 period. It's kind of like the George Carlin
skit about how people blame politicians for society's problem, but politicians are just as flawed as the society they come from. The people who were born from the '30s onward and raised in the USSR were the homo sovieticus, born and that's been satirized throughout the former eastern bloc as conformist, pilfers from workplaces for the black market, doesn't take care of collective property, and lacks personal responsibility. Paradoxically the USSR needs a leader who wasn't born in it, Gorbachev was the 1st Soviet leader born and raised in the USSR and he set the stage for its implosion.
Nationalities questions would probably be less pressing on balance. Without the poison pill of annexing western Ukraine, Moldova, and the Baltic States, the nationalists sentiment of western Ukraine would have had a harder time "infecting/spreading to" eastern Ukraine. Belarusian national consciousness would have a chance to develop without the deaths of WW2, but Belarus is small enough to not threaten the USSR's existence. There would probably be more East Slavs relative to minority groups. The Chechens, Tatars, and Volga Germans would be more numerous and culturally rooted without the deportations of WW2.
I don't think the Central Asians would have caused too many secessionist problems, in the 1991 referendum on the USSR they were strongly in favor of keeping the Union. Regional comparisons are important, independence probably looked like the chaos in Afghanistan for central asians, whereas the Europeans SSRs had prosperous nation states to look to as a model. The myth of the Victory WW2 was important for Soviet identity, and it's the founding myth of modern Russia. Without it the Revolution, Lenin, or Stalin may play a larger role. State admiration of Stalin would help keep Georgian separatism in check, he still has high approval ratings there today.