There are really two questions here that make the answer somewhat of a paradox. Essentially they are 1) Did people at the time realize it was coming to an end and 2) In hindsight, can we see things that indicate it was coming to an end.

I'll answer in brief first.

I think the answer to question one is that, in fact, it was not at all obvious. And the answer to number two is that it's almost ludicrous in hindsight that it wasn't obvious.

Alexei Yurchak's book Everything was forever until it was no more is the best book on the Soviet 60s-80s in my personal opinion because it deals explicitly with the aforementioned paradox. He actually argues that this paradox is one of the things that kept the Soviet Union afloat. As Yurchak says it "A peculiar paradox became apparent in those years [the years of collapse]:although the system's collapse had been unimaginable before it happened, it seemed unsurprising when it happened." (pg. 1).

Yurchak calls the end of the 50s-80s "Late Socialism" and argues that it was characterized by a "performative shift of authoritarian discourse and the subsequent normalization of that discourse." (pg 31) In other words, performing and reproducing the rituals, ideology and structure of "late socialism" made the system seem very robust or eternal and unchanging. This was a departure, according to Yurchak, from the earlier authoritarian discourse was characterized far more by a dialog between ideology and practice. In contrast, late socialism, to put it another way was less about the MEANING of the rituals, ideologies and structures but rather saw the reproduction of them as an end in itself. But, importantly, the lack of meaning wasn't entirely obvious until after the fact.

There was plenty of evidence, widely publicized, that the Soviet economy did not work and civil society was in sharp decline--I remember reading about declining life expectancy, lack of consumer goods, general collapse of civil society. But the military and space programs kept up with the US, and we here in the US I think almost without exception were caught by surprise when Party rule collapsed. (I am not sure what it means to say the Soviet Union collapsed.)

I visited the Soviet Union in 1991 with a delegation of American lawyers, we met with Gorbachev and members of the Supreme Soviet to talk about their desire to liberalize their legal system. The Berlin Wall had fallen, most people now would say the Soviet Union had already collapsed, but it didn't seem so at the time. I don't think many of us in the delegation thought it was at an end. Those who were talking about its collapse were delegates from the Baltic states, and the very energetic Russian business people who were sure that Russian national independence would soon be a fact. The Communist Party had ruled by terror for so long, and the Red Army was still loyal to the party, and most of us thought that would continue even if there was some movement toward national home rule. At the Supreme Soviet there was talk of forming a more modern federated system, with the introduction of some political freedom and easing economic controls--Glasnost and Perstroika. Gorbachov spoke to us of his hope the Soviet Union would remain intact but would liberalize, become a modern state instead of a totalitarian system. His plans collapsed, I think mostly through the incompetence of the Communist party and the decision of the Army officers not to follow the Party commands to repress the Russian movement to democracy.

I guess this comment might be anecdotal, but I do have somewhere the printed proceedings of the conference in the Kremlin, notes of what Gorbachev said at dinner, and some of the participants wrote about it afterward. Reports of the decline in the economy and civil society were common, although I only recall one overall report published in New York Review of Books sometime in 1980s. . . . BeatrixVonBourbon's account of public sentiment, esp disaffection of young people, corresponds with my own recollections, for what they are worth. TenMinuteHistory I think is speaking of ruling Party apparatus, those I met and those who spoke to us seemed to be reciting formulas without any connection to reality (like the five year plans that were supposedly being fulfilled, and were openly joked about).

There's more than one paradox in your question. TenMinuteHistory's excelent answer on how the inevitability of the Soviet Collapse only seemed that way after it happened it one, but of course the other side is that the collapse of the USSR and its inevitability (or lack thereof) was viewed differently from either side of the Iron Curtain.

From the Soviet Side, TMH's response is prefect. That which was the Soviet state from the point of view of the people who lived within it seemed fairly strong and robust even as it rotted from within. By the 1980s the Soviet government, despite maintaining much the same appearance as it had during its Stalinist hey-day was a shadow of its former self though, one looking only at appearances could easily miss that.

But from the American side it's a whole different beast. The Kennan Telegram -- and we can fight until we're blue in the face over whether George Kennan was right or wrong -- ultimately predicted that the Soviet Union would, indeed must, fall if it failed to expand. With a few exceptions the United States categorically achieved the strategic objectives set forth in the X-Telegram. Yes, some nations "fell" to Communism but they were, for the most part, few and far between and rarely of great geopolitical significance.

Had the Americans put any real faith in the document upon which almost their entire Cold War grand strategy was based the USSR's fall would have seemed a foregone conclusion by the 1980s yet Reagan stormed into the White House with rhetoric of an Evil Empire.

Yes, Reagan's rhetoric was somewhat self serving (as was Kennedy's and Nixon's etc etc) but people believed it. The United States funneled billions -- nay -- trillions of dollars into high tech defense projects (many of which are still around and making headlines today) to defeat a Soviet menace that was, by no means, seen as a paper tiger.

Now by the time the Berlin Wall came down there was a little more of a sense that there might not be a lot of time left for the Soviet Empire, but that's another story.

It can be argued that Gorbachevs Glasnost and Perestroika were intended to be a pressure valve of sorts, a way for the government to appease people but remain in control. Some may view this as a sign of desperation by the Party leadership.

The 'pulling away' from it's satellite states during the last years of the regime may also point to political and economic instability, reliant as it was on exports and USD contributions (the latter from East Germany especially, oweing to 'people trading' with the West), but this could have also been viewed as a tactical retreat-and-regroup scenario.
Additionally, the Soviet leadership was unstable during the 1980s, with 4 changes of leader with it's attendant changes of allegiances and cronyism.

Public unease would have made itself most apparent in the reactions to shortages and deprivation. The Communist economic model was planned and central based, meaning all production was based on last years output, and so was notoriously ill-equipped for the emerging modern Soviet' needs. Younger Soviets were also becoming increasingly aware of Western standards of living and freedoms, thus fueling more resistance from this age group not just in the USSR but all over the Eastern Bloc.

The economist Ludwig von Mises wrote a book in 1920 called Economic Calculation in the Socialist Commonwealth which analyses the sustainability of the Soviet centrally planned economic model.

Mises, and Hayek even more, saw prices and price variations as a system of distributed information and intelligence. Understanding this is key to fully get to grips with the Misesian view: prices contain within them essential information that optimises the entire human interaction system's allocation of resources according to an ever-changing price matrix. That price matrix, the aggregate information contained within all market interactions, is absolutely essential for an economy to function.

It follows that the more prices, demand and supply for goods and services are determined by a small group of people, rather than by the trading interactions of millions of market participants, the more inaccurate and unsustainable the matrix it will be.

This isn't because of some bias the small group of controllers might have due to personal interests (although that is always going to be a factor), but simply because they have only a fraction of the total information available to them, compared to the aggregate information contained within the market as a whole.

Mises arrived at an estimate that the Soviet system was unsustainable because of the compound distortions in the price matrix the system relies on. Hist estimate was about 50 to 60 years. It is argued by some Hayekians that the Soviet system lasted another 10 to 20 years because the administration still had access to indirect pricing information essential for the efficient allocation of resources, information it received from market-based economies in the rest of the world.

When you say "not sustainable" you mean economics and industry or curbing Baltic, Caucasus countries?

The Political Science establishment didn't see it coming. They missed the Mauerfall and the Collapse of the Soviets. It's a well known trope in the field.

There are two parts:

1.) most observers completely missed signs that the USSR was about to collapse...

2.) most observers expected the fall of the USSR either to be bloody, or preceded by an attempt to invade their way out of their problems.

Honestly, that the Party's coup against Gorbachev failed bloodlessly was just as surprising as everything dissolving so fast.