Short answer- until it passes or causes an obstruction. I have a cat with Pica and it's no joke. I'm glad you are working with a vet on this one. It might be worth contacting the shelter where you got the cat just to inquire. Say you think the cat might have pica and ask if the previous fosterer had the same suspicions or if they noticed anything. Getting a history of this kind of behavior is useful to your vet. I found that ingestion of materials is taken too lightly by vets until it causes a problem or is expressed as an ongoing problem behavior so knowing if this is something new or something old really does matter. My pica cat is fine btw. We have him on medication and are very tidy and so he is doing well.