If you've got a search that contains more than 1000 prospects, you'll have to break it up into fewer pieces. You can do this easily by filtering your search, here's an example.
This search contains 1,548 leads, however, if I add just two functions, I get this list to 810 leads, awesome! I can now scrape this list.
Then, I'm going to exclude these two functions, and get the remaining 738 leads. This way, I've scraped all 1,548 leads.