The word robustecían is the imperfect form of robustecer in the third person plural.
See the full robustecer conjugation

robustecer

Además, algunas prácticas religiosas y costumbres, reforzadas con políticas oficiales, robustecían aún más y daban validez a la discriminación y perpetuaban el ciclo de opresión de las mujeres.
In addition, certain religious and customary practices, reinforced by governmental policies, further entrenched and validated discrimination and perpetuated the cycle of oppression of women.
Want to Learn Spanish?
Spanish learning for everyone. For free.
SpanishDict Premium
Have you tried it yet? Here's what's included:
Cheat sheets
No ads
Learn offline on iOS
Fun phrasebooks
Learn Spanish faster
Support SpanishDict