Falco punctatus which is endemic to the forests of Mauritius is currently listed as ENDANGERED in the Red List of Threatened Species of IUCN. The species can be saved by restoration of its habitat, complete ban on the use of pesticides and by checking the invasion of introduced plant species.

This is a critical question which, sadly, is being raised by increasing numbers of dwindling species.  I am no geneticist but believe the record - without resorting in extremis to DNA cloning (with the same genetic concerns you mention and, no less, the technique's controversy) - is not entirely bleak. The Californian Condor was down to only 27 individuals, for example, and I think creatures in even more dire situations are also recovering.  Don't give up!

Yes, a population decline like that experienced by the Mauritius kestrel results in all sorts of genetic problems.  Wild population recovery is relying on a tiny number of individuals, including just a single female, and this kind of founder effect can greatly impede the genetic health of the future population.  However, sometimes there is a positive outcome from such drastic population declines in that deleterious alleles can often become purged from the population, so that offspring are not inhibited by the negative effects of such genetic aberrations. 

As you know , it is endangered species only the way to protect the species by protecting its habitat. I am fully agreed with Arvind kumar. It is not possible to stop the natural phenomenon . Eventually, it will be happened .

The species was saved from the brink of extinction with only four individuals left. Hence, the original genetic pool was very small which would affect robustness of the subsequent generations to survive environmental changes. However, it can also be argued that the remaining individuals in 1974 were among the fittest, hence increasing the frequency of the "fittest genes" in the population. The gene pool is also slowly increasing with time as random mutations occurs. 

If no concrete action is done to improve their habitat quality and provide them with a greater habitat range, the population might indeed crash at some point. 

http://www.iucnredlist.org/details/summary/22696373/0

I do not think that the 'fitness' oi the surviving individuals is the issue; the hidden deleterious recessive are (and the general lack of heterozygosity).  I agree that inbreeding depression has a tendency to be transient, and that if humans help the population through these 'purging' generations, the species may come out alright with respect to inbreeding depression (although it will still be generally monomorphic).

An additional positive factor: the Mauritian falcon population has probably always been relatively small (a top predator on a small island), and may already have done some of this purging naturally. And as for a lack of heterozygosity, cheetahs have been essentially monomorphic for something like 10,000 years, and were doing just fine until moderns humans started killing them and destroying their habitat over the last couple hundred years.

After 40 years, I agree with Dr O'Brien: genetic purge may have been effective, especially if reprodution is successfull nowadays. The experience in domestic chickens points to high inbreeding coefficients in family owned stocks (with a single male at a time). On the other hand, the limited variability is evident and it can affect adaptation in changing conditions.

Your contributions have been really helpful.

Thank you.

This Beeb article calls into question a seminal biblical tenet and is general for this forum.  But it poses fundamental questions and sheds some light on the complications of the issue Sheik posed.

http://www.bbc.com/future/story/20160113-could-just-two-people-repopulate-earth

Sheik, here is another article that that offers some hope.  The epigenetic effect is particularly intriguing.

http://www.nytimes.com/2016/04/26/science/channel-island-foxes-least-genetic-diversity.html?hpw&rref=science&action=click&pgtype=Homepage&module=well-region®ion=bottom-well&WT.nav=bottom-well