Sure, they lost Soviet backing when Gorbachev pulled out, but did they not have enough police and military to preserve their own positions through violence after the fall of the USSR?
I know in some countries like Romania the army turned against the government, but this wasn't the case everywhere, was it?
Wasn't there at least one or two regimes who retained control of armed forces, but liberalised anyway?
Why would they do that? Wouldn't it be in their best interest to keep a tight grip, especially when they saw what happened to the other regimes that tried even partial liberalisation?
Retaining power cannot be achieved through repressive capacities alone, there has to be, even if its just a minute section of the population, a level of legitimacy seen in the government by its people.
Giving an answer regarding why the Soviet bloc (the name for all the so-called ‘Soviet Satellites’) collapsed is impossible in such a short post, as each country had significantly different relations to Soviet socialism. For example, Hungary became part of the Soviet Bloc because the communist party won a national election shortly after the war, after which they cancelled future elections and replaced them with ‘direct democracy’. Comparatively, East Germany / the German Democratic Republic, came into the Soviet Bloc as part of the end of World War 2 deal with the Allies, and the people accepted it because they felt it was provisional and would help prevent a Third World War, which was believed to be a distinct possibility in 1950s Europe.
Against what is commonly considered in popular discourse, the Soviets did not just rule through pure repression (although censorship and repression were prevalent to varying degrees in all of the Soviet Bloc). Many did benefit, to a certain extent, from the introduction of Soviet socialism, which helped to industrialise many previously agrarian economies and assisted massively in post war recovery. However, by the 1960s many of the countries in the Soviet Bloc became stifled by the bureaucratisation of life, the inability to adapt in society and economy. Although there wasnt as stark an opposition to socialism as is most commonly discussed, its reliance on a centralisation by personnel completely detached from everyday realities led to the black market becoming more of a friend to the people than the state industrial complex. By the 1980s, the economy was past breaking point, such that at the turn of the decade, many of the governments had little left to fight for.
Furthermore, the key to answering the question of legitimacy is identity, and almost none of the ‘satellites’ identified with Soviet socialism. Socialism in Central and Eastern Europe was always associated with the Soviet Union, such that the governance was always seen as foreign and therefore people rarely identified with it. This is unsustainable, and by the 1980s the governments could not convince the people that they represented their interests. Comparatively, the likes of Cuba had introduced socialism in a popular movement that continues, to this day, to be considered part of the national identity.
This is a very brief summary (due to it being very complex) but I hope you can see that the reality was that the question should not be so much why didn’t the governments cling on to power longer, but how did they cling on to power for so long...
If you have any follow up questions I would be happy to answer, and I hope that helped!