I'm sure that there is a timer. How about dividing things up into multiple objectives, in a series? Like:
- Become a guardian (success: guardian = yes)
- Have a ward who is ten years old
- Have a ward who is sixteen years old
Just an idea if the AI proves too stubborn. Could mix it with things going in the ward's life. For example, 'See one of my wards become a squire' or 'Make my ward a knight'. And then once he or she turns sixteen, your former ward still has the 'mentor' opinion modifier towards you so you could create objectives/decisions/events for an ongoing relationship. 'Get my protege a job' for example.