There can be many reasons why your Mattress Firm Credit Card application was denied. In most cases, it's one of the following:
Your credit score is too low
You don't have enough income
You have too much debt relative to your income
There are too many recent inquiries on your credit report
There's a recent delinquency or error on your credit report
Unfortunately, you cannot ask for reconsideration if your application gets rejected. You should consider becoming an authorized user on someone else's account, instead. Alternatively, you can apply for a secured credit card that offers better approval odds.