It's NOT you OR the card!
I've had this happen WHENEVER I buy a new iOS device -- when I bought my iPhone, my partner bought his, AND when I bought my iPad. Seems adding existing accounts to new devices is particularly problematic. I was *hoping* to find an answer here and not just more questions, but when I saw everybody saying you must have fat-fingered the card # I had to speak up. My partner got his phone switched out today due to the flash washout issue and it happened AGAIN! same account didn't change card #s or anything .. Its been working fine, and bam! His new device asks him to ONLY enter the security code for verification -- and fails. He only had to enter 3 numbers, not change anything else, and I've got the card and have been using it in iTunes TODAY with no issue -- suddenly it starts failing for BOTH of us the minute his new device comes online -- so, it's an issue with the store, not you or the card. Usually "fixes itself" after a couple of days. Try entering another card -- then switchIng back -- that has occasionally worked for me.
Hope that helps!