There are many books on the USSR's collapse, but I'll point to Kotkin's Armageddon Averted as a source.

The short answer is that up until the August 1991 failed coup most of the Central Asian republics were iffy at best about independence and the Kazakh SSR was outright opposed due to Kazakhstan's economic dependence on Russia. Even after August 1991 there was a major, failed push for a shrunken but still powerful union of Russia, Ukraine, Belarus, and Kazakhstan. Ukraimian skepticism ended up torpedoing even this union and the Union totally collapsed by New Years of 1991/92.

On March 17th, 1991 the U.S.S.R. organized a national referendum for the nation's future. There was only one question on the ballot,

"Do you consider necessary the preservation of the Union of Soviet Socialist Republics as a renewed federation of equal sovereign republics in which the rights and freedom of an individual of any nationality will be fully guaranteed?"

The vote was forbidden by the authorities in the baltics (notoriously anti-soviet), as well as in Armenia, Moldova, and Georgia. The vote was still held in these republics anyway, but the voter turnout was less than 50%. The people who made the effort to go to the vote in those republics would have mostly been pro-soviet.

The rest of the republics had the vote openly, and turnout was around 80%.

The nine republics who voted openly voted 70% in favor of preserving the U.S.S.R. The common criticism of the referendum was in its wording. Some say the voters didn't understand it. Others say that the results established something like the U.S.S.R., but not the U.S.S.R. Here's a nice discussion on it. In the end, though, it didn't matter. The republics went their own separate way and the closest thing to a continuation of the U.S.S.R. is the Commonwealth of Independent States, a sad ghost of the old state, and an attempt to preserve the close economic ties that the republics depended on for survival.

Which is interesting, because the first and only referendum in the history of the U.S.S.R. was ignored. The "victory" of democracy was actually a rejection of democracy, you'll rarely if ever see the referendum mentioned.

The advantage they saw in remaining soviet depended from state to state. Most of the states' populations still believed strongly in the communist ideology (several maintain similar economies today, like Belarus and the central Asian states, although they continue on paths towards liberalization). The benefits of the Soviet infrastructure were also significant. The vast majority of trade happened between states, which still happens today in the form of entities like the CIS and the planned Eurasian Union. nations like Moldova are at a significant disadvantage without the support of the USSR today.

The transition to Capitalism was disastrous for every single one of the nations. Every HDI indicator fell, GDP fell by 50% or more overnight everywhere, populations began to decline, suicide rates went up, technological development and industrial capacities fell. Privatization was literally a robbery of the people, happened chaotically, and was at times directed by predatory outside entities for their own benefit. The result of this is the high degree of corruption evident today in practically every post-soviet republic (notably places like Ukraine and the Central Asian states). Nearly every republic fought one or more civil wars, had violent conflict in some capacity, and has experienced a slew of attempted revolutions.

The U.S.S.R. might not have had the productive flash like the economies of the west (the famous thing being Gorbachev's astonishment at American grocery stores, as questionable as that is), but they worked. For example, allocative efficiency in command economies matched or exceeded the efficiency of their western contemporaries in the 80's.

There was free healthcare, education, and housing guaranteed for everybody. The saying is that there was no food on the shelves of the markets because it was all in the pantries of the people.

It's a lot more complicated than some vague notion of "freedom's triumph" or the collapse of an "evil empire".

What about Belarus? I've had the impression they'd quite like to go back to the USSR - the original post-independence flag (white with a red stripe) was replaced with the Soviet flag minus hammer and sickle and ISTR they keep occasionally trying to get some sort of economic and/or political union going.

Only an impression and straying into the 20-year rule, but any comments?

Between the August 1991 coup and before the December 25 1991, what was the Soviet government doing every day? Was the collapse inevitable at that point? Were they actively fighting to keep the union intact?

Many of the soviet republics were against the dismantling of the soviet union ( mainly in central asia and in particular kazakhstan ). Gorbachev was also vehemently against the dissolution of USSR. Unfortunately for him, Yeltsin was far more competent than he was and gorbachev was marginalized in the only soviet republic that mattered. Kazakhstan was pretty much the last to "leave" - and by that, I mean everyone else left and they were the last one standing. I believe they didn't even sign the law dissolving the USSR.

Some of the benefits were military protection, stability, markets, free movement/travel, education, progress, etc. Not to mention it kept interethnic fighting and rivalries at bay as long as the USSR existed and russia was in control.