Some websites go out of their way to prevent passwords from being stored by web browsers, but such blocks are often browser-specific. Thus, we would need to know which newspaper website it is in order to check out the source of the issue ourselves.
Let us know.
I am using OS X Tiger and Firefox 3.6. I can't get Firefox to remember my password to a newspaper website. Remember passwords is checked, and the site is not on the exceptions list, and workarounds involving an extension or bookmarlets don't seem to do anything.
Safari has no such problem with the same site, but I'd rather use FF.