I am having this problem. When I try to get the links posted by the user or page it works fine for all, except for high traffic users or pages like 'thebeatles' or 'ladygaya' or'machaeljackson' etc.
One thing we found out was that when you fetch links through graph api, it gives all the comments and evrythign back. In case of celebrity pages, there are thousands of comments, whcih are returned back, and cause to throw a curl exception.
So we switched using FQL and its better as it just provides the links, but in this case also FQL does not work for celebrity accounts. We just can't seem to understand why?
Did anyone come across this problem or know of any way to solve this?
Is it possible that you're trying to retrieve so many comments that it's timing out on Facebook's side?
Have you tried asking for a subset of the comments using offsets or timestamps? Check the 'searching' section of https://developers.facebook.com/docs/reference/api/ for more information
(disclosure: I work for Facebook in the Developer Relations team)