In Rivals of Catan a player can be forced to discard buildings. If a player chooses an Abbey, do they also lose their University (which has a dependency on an Abbey), or do they just lose the Abbey?
No, they only lose the first card.
There are no dependencies, only requirements that must be met in order to play the second card.
On Page 16 of the rules it states:
Once the card is played and the requirement is satisfied, the requirement has no further effect on play.