I came across this while developing my own widget a while back. It turned out the widget was generating a PHP error, which was cutting off WP's processing of my saved changes. But for whatever reason, the PHP error message was showing up in the HTML source but not on the screen, I don't remember why. There are other things that could cause this, but it's possible one of your widgets is causing a similar error. So just to check:
Go to your widgets editing screen. Make some changes to your widget settings and save them. If they DON'T save (i.e. if this problem persists), view the HTML source. (Check your browser's Edit and View tabs, depending on which browser you are using, for a "View Page Source" or "Source" option.) Scroll all the way to the end of the HTML source. Does the last line in the source contain an error message, or just normal HTML code? (You don't need to know HTML to answer this question--if it's an error message, it should be pretty obvious.)
If you do have an error message, try disabling your widget plugins one at a time to see which one is causing the error. You'll probably be able to tell from the error message which widget you need to disable.
Again, this might not be the problem, but it's something I've run into in the past.