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Even for the biggest alliances in Eve Online, having a rich history, the overall team spirit, common purposes and motivation of each individual player are very important. If the alliance doesn't have these things — it is doomed. This happened, for example, with the alliances GoonSwarm, Band Of Brothers. No alliance is actually insured from a collapse — and it all begins with small things, such as silence in the corp chat, low activity of players. There are several ways you can avoid it, and motivate people to play actively.
The social component plays a major role in the life of the alliance. In simple words, -  communication. While the chat is full of life, while the co-allies communicate with each other, while they are interested in communication with each other - the alliance is alive. A leader must struggle to maintain this communication, to direct it to the right track, take actions to keep the people's interest.
The overall well-being of the alliance and managing its income is also important. There are many options for keeping players happy about the alliance related and depending on the corporate income - compensations for the ships lost in a battle, material rewards for the best pilots, rewards for contribution to the Alliance, various contests. If the alliance management generously hands out Eve ISK for the fact that you just play well the game which you love, it will undoubtedly attract talented pilots.
Attracting new people is an important point. No matter how good the original lineup, the core of the alliance was - it is not eternal. Such is life, people leave the game, things change in their real life — work, residence, they spend much less time online etc. - and that's all, people stop playing. This is just a fact, something permanent. The solution is only to attract more and more talented people. Not necessarily the best pilots — a beginner playing for 1 month who constantly encourages the entire alliance in the chat, is a very valuable player as well.
An alliance leader must understand the value of each player. Encourage the best, put them as an example for others - and success is inevitable:)