There are many Hassidic discourses regarding this idea, foremost among them The Baal Shem Tov (father of modern Hassidut) who read the passuk slightly differenty. A Tzaddik will instill life through his Emunah. One thing that many of the sources have in common is a fact I've often overlooked, which we'll try to develop a little below.
The general dynamics of the fall and recovery go something like this: In order to attain a new level, HaShem takes away the Tzaddik's current status, and he's left with nothing but a shell of his former level. The Tzaddik, through his Emunah, continues to act and serve HaShem from the little that remains of his previous level, holding out as long as it takes until HaShem grants him a new [and higher] level.
In the past, I've always understood this to mean that the Tzaddik basically holds on, fighting with whatever strength he has, taking advantage of whatever he can in order to tread water (as it were) until HaShem recognizes the Tzaddik's faith and throws him a rope. (so to speak) Recently I noticed the recurring theme (in many of the Hassidic texts) of how the Tzaddik continues to serve HaShem specifically from the shell of his former level. When you emphasize that point, the whole exercise goes from a flailing free-for-all to a focused discipline of sorts. The Tzaddik serves HaShem [davka] from his previous level, focusing all of his energy on the certain knowledge that HaShem can be reached through the particular door that would seem to have been shut. He pursues tirelessly until he succeeds in revealing what HaShem hid from him.
Think for a second of the way a parent teaches a toddler, an example often used in this context. The father takes a step away from the child in order that he will try and take a step towards his father. Then the father takes two steps and so on. For the toddler this experience can be infruriating because all he sees is his father repeatedly abandoning him. It is only the reward and excitement that he receives as feedback when he makes it to his father that fuels him forward. Now take a toddler with the intellect of a twenty-year old. The toddler understands his father is teaching him a lesson, and may even understand that its a worthwhile lesson.
The Tzaddik is like the toddler (lehavdil) who understands and knows it is a lesson, and is striving to learn the lesson. The Tzaddik knows that if a path was open and now it's closed it is only so that he should strengthen the "muscles" of that path until he can open it again. When that path is once again open, when that "skill" is freely available to him, he will pursue HaShem in new ways, always pushing always growing.
This is one difference between the Tzaddik and the rest of us. We don't know we're toddlers. We flail around and get bored, try to pursue other things that have a lower threshold of pleasure. Things that aren't teaching us as much. "No pain no gain," has a lot of really deep truth to it. (Though it can still trip us up when misapplied.)