wow...good one! it might just be a matter of opinion: at first i thought (there i go again) that the height of soviet influence (assuming your speaking world-wide) could have been the very beginning - stalin's regime had its filthy hands in all kinds of countries following WWII. AND those hands were armed. stalin knew this, and saw opportunity for a land grab. the US, wise to his sinister ambitions of spreading communism, thought seriously and highly enough of the USSR's abilities, that a cold war was started. all policies from then on, transpired according to the original design:
1) get land and hold it
2) use land and people to further influence world and gain glory for the USSR
3) turn world redski
kruschev took official power in 1955 - he was a royal pain for the US. the invasion of hungary, planting commies in third world countries, etc. also under his watch, the soviets tested (succesfully) an ICBM, sputnik I and sputnik II were launched, 1960 they shot down Gary Powers, and 1961, (see above) - i think the reds were feeling pretty bad-*** at that point!!!
i think its a matter of who's personality was the cult at the time, and how many victories in the name of communism fed that cult.
as far as when did the tide turn?
i would have to say the day Gorbachev took power. right from the start, his policy was one of economic change. ECONOMIC = the heart of communism. i believe it was this stealthy, beginning of an attack on soviet style
socialism in conjunction with his policies under "perestroika" that opened the flood gates of change.
WHEW! my tiny brain hurts!