Unfortunately, yes. Part of it may actually have to do with credit issues. For example, if you had a bankruptcy or foreclosure 6 ½ years ago, and the credit card issuer specifically prohibits approving cards to people who have such delinquencies, you won’t be approved.Another important issue is income. If it’s is deemed either too low or too unstable, you can be declined for the card. And yes, it is possible to have both a high credit score and a low income.