Many flights/segments do, some flights/segments don't.
Here's why: in order to get lower fares we've included hard-to-find "unpublished" or "consolidator" fares in our search results. Unfortunately because the price is so low, some of these fares do not qualify for frequent flier miles.
Currently we have no way to automatically distinguish those fares that do qualify from those that don't. (Yes, it's hard to believe, but true.)
If you want to request only flights that do qualify, just reach out to us and we'll get you some options.