What are the limitations on a Twitter saved search?

I am trying to gather tweets on a range of topics, but it seems Twitter searches have a time limit (only go back so many days) or perhaps it is the number of tweets that limits the search.

If it is a very active search, the tweets collected only go back so far and then stop. Does anyone know why this is?

Sorry if I am being vague. I am trying to explain what I want to know as clearly as I can.