I haven't been on Answers for a while. Where are the categories of questions ? Have they been deleted ?

From what I've read / seen, the problem is not with Yahoo Answers, but with your browser. Currently, there seems to be an issue using YA with Chrome. If you are using Chrome, you may need to temporarily switch to another browser for the categories to show up for you.

They should be on the Left Side of the Page if they have Disappeared on you Clear your Cookies and Cache and Delete your Temporary Files then close out your Browser and Reopen it and try again should it still be gone try a Different Browser

If using CHrome, try another browser. Otherwise, do a good cache clean and reboot and refresh the page a few time when you log back in. That usually brings the list back. Some report it needs to be done twice. I only get that glitch when I do a deep security clean on my computer.

They are still there. They are not deleted automatically unless someone on Yahoo Answers reports the questions.

Otherwise if the questions are not reported, you can delete them but only if no one else answers them yet.

Have you tried refreshing the page a few times? I mean I know that probably sounds like a no-brainer but I use Chrome and it's happened to me and I just reloaded the page a couple times and it worked again.