One obvious reason for rejection of application is human error i.e. the error committed by you in filling up the application. These can be small mistakes like a wrong telephone number or wrong name or the postal code might be wrong. It’s normal to make mistakes, after all we are human being and no human being can be termed as perfect. Another strong reason for rejection of a application could be missing mandatory information i.e. when you forgot to fill-in some mandatory information in the application form. Sometimes, the application could be rejected because the application form has been filled-in in a handwriting that is illegible to the people processing your application. At other times, the sales representative (of the supplier) could have made a mistake in either depositing the form correctly or in guiding you in the filling of the application form (newly hired sales representatives can make such mistakes).
However, these human errors are just minor errors that can be corrected later on and hence the only impact would be in terms of the delay in receiving your credit card. The main and the most important cause for rejection of applications is bad credit ratings i.e. a negative credit history. If you have been using other credit cards or if you have taken bank loans/mortgages in the past, you would have already build your credit rating. If you have been making your bill/instalment payments in time (and in the correct amount), you would have already acquired a good credit rating. However, if you have been irregular or if you have been defaulting on your payment dues, you would have developed a bad credit rating. This credit rating is calculated by credit bureaus who receive feeds from various credit suppliers. All applications are checked for the credit rating of the requestor and if it comes up as negative, the application is rejected outrightly.
So, these are the 2 most important reasons for rejection of application and you must pay heed to them (especially the credit rating).