Sustainable is a word overused and over-appropriated to the point of meaninglessness. I wish to use it in a precise sense to describe a state of human existence with the potential to endure indefinitely, so this is my attempt at a good definition.
Definition
A sustainable society is a society which can maintain a population equilibrium for ecologically significant timescales.
Perhaps it is also useful to describe a sustainable process:
Definition
A process is said to be sustainable if it persists indefinitely.
Here I’m imagining one of the flying ships in Conrad’s Game of Life for instance. I’m not bothering to define process here because I’m lazy, but suffice to say it is a periodic function of time.
Actually requiring it to be periodic may be stupid, you could for instance imagine a human society which changes at a slow enough rate as to be ecologically viable but nonetheless is not strictly periodic. Think of red queen.