We updated to 3.9.1 and we are having a similar problem with the featured content widget.
Our site is http://www.scio.com.mx
If I make a change in the widget, I lose the content. If I move it to the Inactive area, clear the cache, move it back and clear the cache again - it shows. However, the featured content rotation has stopped working. I am using a page list for the content. I have five pages in the list. I can't go back to the previous version we were using (3.8.2) because it completely breaks the pages now.
I've tried changing the length of time the content is supposed to show, and several options. Everytime I change an option, I lose the widget content in the widget (i get the title but no content at all). If I go through the routine I mentioned above, it can get it back, but it doesn't change content rotation. We have checked on several different browsers (IE, Chrome, Safari) and we get the same results on everything.
There is some underlying bug I don't understand, but it is making what is otherwise a very nice feature, very hard to use.