Q:

What kind of event would cause the current Mitochondrial Eve to be replaced by a new one?

Apparently all living humans are matrilineal descendants of a single woman who lived 200.000 years ago. She is called Mitochondrial Eve.
But at the time she lived there was a different matrilineal ancestor that all living humans shared. And between then and now I imagine many other women have been Mitochondrial Eves of the human population that lived at a particular time.
What I'm wondering is what kinds of events would cause a different, more recent matrilineal ancestor to become the Mitochondrial Eve of all living humans?
One scenario I can image is that the human population is on the brink of extinction and literally only a few people survive. Because there are so few people alive, I imagine that the chance that they share a more recent matrilineal ancestor is high.
Are there other scenarios possible? Does the chance of a new Mitochondrial Eve emerging decrease if the human population is large (billions) instead of small (hundreds or thousands)? Suppose that the human population will not decrease, is it likely future human populations will ever have a different Mitochondrial Eve than the current population? Does it depend on the amount of people that migrate?
The same questions could be posed for Y-Chromosomal Adam and the most recent common ancestor of all humans, I guess...

A:

One possible scenario would be that a particular woman develops a mutation rendering her much more 'fit' (in the evolutionary sense) than her peers. For the sake of argument, lets take the very simplistic case of an X-linked recessive mutation causing the women who bear it to have say 10 children at each birth. If this mutation is then transferred to the offspring, it will very quickly spread across the entire population. 
If this continues for a few generations, the crushing majority of the earth's population will be the descendants of that one woman who carried the original mutation, she would be the new mitochondrial Eve.
I want to stress that this is nothing but a very simplistic thought experiment. Such a mutation is i) very unlikely, probably impossible, ii) likely to render the carrying individual less fit rather than more as each birth would be exhausting, increasing the chances of dying during child birth.

Update:
I have specified that the mutation has to be X-linked and recessive. This means that it will only present a phenotype in women who are homozygous for it, women both of whose parents carried the mutation. This is because, as mgkrebbs very correctly pointed out in the comments below, otherwise her sons would mate with women who are not their sisters and their children would have the mutation but not her mDNA. If the phenotype is only expressed when the mutation is homozygous, only women whose mother carried the mutation (and Eve's mDNA) would show it and only then would a new mEve arise. 

A:

The new mitochondrial eve is alive right now.
When humans reproduce, mothers pass their mitochondria to their offspring without a contribution from the father.  As a result, each human can trace back their mitochondrial lineage as an unbroken chain to a single individual woman in the past.  Through random chance (genetic drift) or natural selection women in some mitochondrial lines will pass offspring to the next generation, while others will not.  If a woman fails to pass offspring to the next generation then she represents the end (i.e., extinction) of a particular mitochondrial lineage.  As time progresses more and more of the original mitochondrial lineages will go extinct until all humans represent one remaining linage. 
Note that this is a continual process since lineages accumulate differences through mutation of the mitochondrial DNA.  This mutation is the source of the different lineages that that will go forward.  Based on the estimated rate of mitochondrial DNA mutation we can estimate how long  it would take for extant mitochondria to have developed the genetic differences we now see. 
If you take a snapshot of this process at one point in time (e.g., contemporary humans), you can use this estimated time to say how long it would take to accumulate the present differences - that is when the line began.  Due to the continual extinction of extant mitochondrial lines, there is some point in the future where if we were to take the snapshot we would estimate that the mitochondrial eve was alive right now.
EDIT based on comment:
The rate that a new mitochondrial eve would be formed is based on the accumulation of mutations in non-coding regions of the mitochondrial DNA (i.e., the molecular clock) which is dependent on the population size only in so far as the probability that a given mitochondrial line will survive when all others go extinct is basically its initial frequency in the population. So in a large population with more initial diversity each line will have a lower probability of succeeding.  
Also, if there is no selection for or against a given line then changes in frequency are due to chance (genetic drift). In a large population the effect of drift is smaller than it is on a small population.  So if the population size is small, then the likelihood that a mitochondrial line will go extinct is greater and the rate of a single mitochondrial line succeeding to be the mitochondrial eve is greater.

