Gmail can be awfully slow with Web Clips
Peak at the Web Clip from the BBC News site at the top of the screen grab. Gmail is showing me news from 6 days ago. Six day old news is no news. If Google News finds a new page on an approved news source site and it seems to be older than four days then it'll simply be ignored.
I'm not sure why the Web Clip feature is so slow to update at times. I'm sure it could be much faster.