If your credit is too new or if you have too many recent account and inquiries, that would be cause for a denial. Also if you have high utilization on your existing cards. Credit approvals don't soley rely on scores; your entire credit report is taken into consideration.
Your score is only 1 variable lenders consider. If you're new to credit you'd have what people call a 'thin profile'. Good credit age, or a 'mature profile', with lots of good history & credit mix tells lenders you're a responsible and well managed borrower. If you're new to credit I'd suggest you manage your current cards well & search out how to increase your credit lines with them for a while longer. If you can build good history than you'll see more than secured card options soon. 3 cards in 6 months could cause lenders to see you as 'hunting' for credit & may view this as an additional risk. Give it time, mature your cards, & soon you'll see better offers.
What 3 cards do you have? I'm guessing they are all retail cards.
As the others have suggested, your FICO scores aren't the only things a creditor looks at. Your file appears very young and very thin...hence the secured card recommendations. What I believe is that you need time for your accounts to age.
In addition to the factors already mentioned, lenders and CC issuers consider factors outside your scores, notably income and existing debt. We don't know the dollar value of any existing loan balances you might have nor do we know your income.
A person could have low CC utilization, accounts that are several years old, and scores in the 800s -- and be denied (or offered very limited products) due to low income, high existing debt, or a combination of the two.