I checked the outbox and I see emails for several of those widgets having been sent.
There are multiple outgoing emails for BBC and CBS today.
I'm not seeing outgoing email from some of the rest - I've checked the server and the email functionality is enabled for all of them. The widgets *might* be short-circuiting if there's no actual link to send. Some of the widgets scrape the content in the absence of RSS and may not be properly picking up the links, and in some cases, the RSS is so degraded that they sometimes don't have links either.
In any case, given that these widgets worked in the past, and don't now, with no changes to either the widgets or the server, while other widgets work fine, points to changes in the upstream feed.