Okay IMO this is a tough one to understand if I put myself in the shoes of a non native speaker.
I'll try to explain:
Sustenabilidad and sostenibilidad roughly mean the same most of the time, but they have nunances between them that make them slightly differ in meaning.
You won't find sustentabilidad in the RAE but sostenabilidad is present:
- f. Cualidad de sostenible.
Now, sustenabilidad comes from sustento which is in the RAE:
m. Mantenimiento, alimento.
m. Aquello que sirve para dar vigor y permanencia.
m. Sostén o apoyo.
To understand sostenibilidad we have to define the word in its meaning sostenible:
- adj. Dicho de un proceso: Que puede mantenerse por sí mismo, como lo hace, p. ej., un desarrollo económico sin ayuda exterior ni merma
de los recursos existentes.
Sustentabilidad is specific of a external source of support and maintenance. It means that the resources of survival or maintenance are external to it. Example: La sustentabilidad del humano depende del agua y alimento disponible. Example2: El sustento del niño viene de sus padres.
Sostenibilidad is specific to independence of maintenance. Of self survival (sort of). Means, more concretely the capacity of something to sustain itself. Example: Un bosque es sostenible solo si no hay peligros que amenacen su existencia.
Now here is an example that can illustrate both points and their difference at the same time:
La sostenibilidad de una colonia de hormigas depende de su sustentabilidad.
(Okay the example is not as good as I imagined it. But if someone has a better one feel free to edit the answer.)
Now for the terms persistencia and tenacidad is really hard to know if they where used in the 80/90s. But I found a work about Colombia that uses the word several times while describing the economical and social situation. Source: Colombia en el cambio de siglo
The two terms, sostenibilidad and sustentabilidad are widely used at this time to express environmental problems. And it has always been used for economical context since I can remember, when I was in school or highschool we always used this term in social studies or in biology for environment related problems.