Hi Daf,
As you said, only Headlines feed it not fetching feed items and rest all are working fine. This is because you already have the Entertainment, Sports, Politics feeds configured ( all from the same news site ) and they are fetching and importing the items just fine.
When I checked the Headlines feed, I found that it had 7 items inside it, which were already imported by other feed sources. Headlines is nothing but a sub-set of main news from all the news categories. Therefore our plugin is not creating duplicate posts when it has already found that the same post has been imported before.
Let me know if you have any doubts or queries!
Regards
Chirag Swadia