1. to support, hold, or bear up from below; bear the weight of, as a structure.
This implies helping someone, and the religious organizational example might be the two men who held up Moses' arms during battle. It implies cooperating with someone in what they do and helping them do it.
2.to bear (a burden, charge, etc.).
In the Church, this means helping to run the organization - doing something to take a portion of the load off of others, often by assignment ("charge"). This is associated generally with callings.
3. to undergo, experience, or suffer (injury, loss, etc.); endure without giving way or yielding.
This implies standing by someone, often through difficulty. This has many applications within a church setting.
4. to keep (a person, the mind, the spirits, etc.) from giving way, as under trial or affliction.
This deals with providing support of some kind, so another person doesn't fall, fail, etc. This includes constructive criticism and counterpoint, and I have sustained a leader by disagreeing on more than one occasion. In fact, I believe it is impossible to sustain someone fully without understanding and accepting this definition.
5. to keep up or keep going, as an action or process: to sustain a conversation.
This deals with on-going commitment - not just "sustaining" now and then, for whatever reason.
I would appreciate any input about how you view any or all of these aspects of sustaining leaders.