This happened to me on a new profile I set up for a client. Here is how I got around it.
1.) log out of Google.
2.) go to the profile, click on the Q&A link, and hit the ask a question button. Google prompts you to log in.
3.) log in with the account that manages the profile.
4.) Google will now let you enter the question.
5.) log out and repeat.
Then repeat this process to input the answers.
I was afraid that all the logging in and out would trip some security check, so I did the input in small batches (4 at a time), with a 10 minute break in between.
The questions and answers only appear if I'm logged out of Google, or if I look at the profile while logged into an account unrelated to the profile.
If someone has a better solution, please post it.