The following discussion of stability follows Zhang and Guest, who state, "Stability is related to level of self-stress and material properties." 
Minimum Energy Stability (Rest State)
A structure is considered stable if and only if, when subject to small disturbances, it returns to its original configuration. This occurs when the structure's configuration is a minimum energy state, and disturbances lead to an increase in energy that can then be shed.
Assume that the stiffness of members is infinite compared to level of self-stress. If the structure is stable in this case, then it is said to have prestress stability. Any stable tensegrity has prestress stability, but the inverse is not always correct.
Super stability is unconditional stability, regardless of the level of self-stress and material properties. It is the preferred stable state for tensegrity structures.
Instability Due to Divisibility
Some tensegrity structures can be physically and mechanically divided into several identical substructures. If these substructures have relative motions, the original structure is obviously unstable.
Links and References
(1) Symmetric Prismatic Tensegrity Structure Accessed 22 Feb 2010