Infinite password prompt won't allow app download
I have an iPhone 3GS and iPad 1. After latest software update, I can't download free apps. When I install new free apps, I get the "improve apple ID security" prompt to add security questions. When I choose "continue," I get a prompt to enter my apple ID password. After I enter it correctly, there is a shift to a grey page with "loading" and again I am prompted to enter my apple ID password. After entering it correctly, each time the same prompt returns over and over again. End result - I can't download any new free apps (I haven't tried paid apps since this started). I was able to download free updates of existing apps before this happened. Please help.
Thank you.
iPhone 3GS (8GB), iOS 5.1.1