Chat's been broken if you open or close it since the initial patch. If you go into Chat Options you'll usually see that none of the Streams are selected... if you select Area in the drop down box (even if its already selected) and hit accept that should do the trick.
After one of the last patches my streams were all cleared on all my characters and when I checked one or all of them and hit accept the client crashed. I ran a full system check and the client doesnt crash anymore but it doesnt save the settings. If I go back in the are all unchecked still. Tried the safechat with no luck. Theres a post in the tech section that mentions deleting your character profiles but im not doing that since ill lose my hotbars. If you dont care about losing your hotbars you can try that.
Sometimes it resets for one reason or another. I find if I click the little chat bubble icon at the top of the chat, goto options, stream, and then select all but the last 2 options that it sets everything in chat back to normal.
I think it "Breaks" when you mess with anyone on /ignore, or any other chat settings.