Stalin had manages to isolate Trotsky from Lenin’s funeral, this would mean that no major representative of the Left attended Lenin’s funeral, this would have made Stalin generally look a stronger candidate as opposed to Trotsky who did not attend. This is also a similar case for the 13th party conference, were Trotsky was isolated and his policies humiliated. Stalin managed to make sure all Trotsky supporters did not have voting positions within the party to make change. This would have isolated Trotsky who would have needed as much support as he could get to stand up to Stalin.
Trotsky, who seemed to be one of the more natural future leaders other than Stalin had his personal flaws; Trotsky was an ex-Menshevik, the people saw him as a traitor and thought he only joined the Bolsheviks because he saw them as the group that was going to win and become leader of Russia with, Stalin used this against Trotsky, making him seem like a less patriotic and loyal Bolshevik. It also made him quite unpopular on the politburo too. Trotsky did not properly understand that Stalin was such a threat, linking to his arrogance. He thought that he alone would be leader and that he would not have to worry about opposition. In Russia at this time, there were a lot of anti-Jewish feelings by the public. They were not ready to see a Jewish leader. This made him unpopular on the politburo, having the support of the politburo would really assist him in the leadership battle, but seeing as though Stalin had more support from within the politburo this is a significant reason why. He failed to understand that in order to launch an attack a power base is essential and Trotsky failed to build one even after Lenin's suggestion in December 1922 that they build a 'bloc against bureaucratism in general and the Orgburo in particular'. Trotsky’s attack on Kamenev and Zinoviev in 1924 in his Lessons of October convinced them of their need to fear him and made an alliance with Stalin more likely.
Zinoviev and Kamenev attacked Trotsky’s authority; Stalin refused to get involved in the heated debates and therefore kept his reputation intact. Therefore no-one saw him as a real threat before it was too late. Furthermore Stalin had little truth and was willing to undermine his opponents and use dishonourable tactics in a bid for power such as after he had defeated the entire Left Wing subsequent to the Fourteenth Party Congress in 1927 Stalin launched an attack on Bukharin, his only remaining rival. He arranged for a plane carrying Bukharin to be delayed to prevent Bukharin attending an important meeting. Additionally Stalin also circulated false rumours that he was to form an alliance with Zinoviev and Kamenev, as Bukharin organised a secret meeting with the two, Stalin leapt onto publicly accusing Bukharin of factionalism in the hope people would turn against him, which meant causing divides of groups within the communist party who aim to control or influence party direction. As a result Stalin scheming manipulations in preventing opponents from attending important significant events whilst quietly developing his own powerbase allowed him to undermine his opponents authority which made Stalin gain an increasingly positive public image. Stalin creating such accusations meant that the only person whose reputation wasn’t as tarnished was his own. Although morally this reflected badly on Stalin to those in the party that may have known that Stalin was not being honest about his opposition, it made him seem the most clean, honest person for succession.
The failure of Zinoviev and Kamenev before 1926 to recognise that the real threat came from Stalin and not Trotsky is a important but like Trotsky, they had misunderstood Stalin. They also underestimated and failed to appreciate the skill with which he had built up both a power base and a reputation for moderation within the party. Stalin also realised the basic popularity of the Left's rapid industrialisation programme and its antikulak policy and he was quick to adopt these once he had defeated the Left. Bukharin stood no chance against someone of Stalin's ability especially when he was so pro-peasant. Stalin raised concerns over his thought and managed to get Bukharin kicked out of the central committee in 1929.
In conclusion, I would say that although the failure of the Left opposition is not the sole reason for Stalin’s success it was a very major factor to put into consideration. It was Stalin that made sure that it was not successful; he did not allow Trotsky supporters voting roles, meaning more people would be likely to support him. He managed to use concerns about the left / right to get opposition kicked out of the central committee and the politburo.
A lot had to do with the personal weaknesses of the individuals too, Trotsky did not realise that Stalin was actually an untrustworthy enemy due to his arrogance and self-confidence. Zinoviev and Kamenev did not recognise that Stalin was so important. However, the most important reason is that Stalin had better political power and he could apply this better. Lenin’s legacy the he left Stalin behind helped him gain victory too. He could use his power from the central committee and the politburo to make necessary allegiances. Trotsky did not have the party power that Stalin did to make such moves. The other opposition were ultimately too naive to the plans Stalin had in mind.