Naive versions of the diversity-stability hypothesis probably aren't true and do not provide a solid conceptual basis for arguing that conservation of biological diversity is an important goal. A less specific version, one that defines stability as a dynamic property related to the degree that the components of a system determine their own future state, provides a plausible basis for the hypothesis. Unfortunately, this version of the hypothesis verges on circularity and is almost immune to empirical investigation. Moreover, a system that is ``stable'' with respect to some perturbatons - hurricanes, drought, or other extreme weather events - may not be stable to others - invasion by exotic plants or animals, extinctions of component species, or other biotic changes. As far as practical conservation applications are concerned, it is not obvious to me that the diversity-stability hypothesis provides anything more than a useful heuristic.
There is something to the idea of biological integrity. Changes in species composition and community structure may alert us to underlying changes in ecosystem processes more quickly than directs attempts to measure these processes. Diverse systems provide more indicators of change in these underlying processes and if we can manage the systems so that they are protected, then the underlying processes will remain intact, too.
Chapin et al. [8] summarize it this way: