According to the following article, you should wait at least 90 days to reapply: http://www.yourcreditnetwork.com/blog/DeniedCreditCardApplicationsHowLongToWaitBeforeReapplying.aspx
Here’s another good article I found, called “Credit card application rejected? 3 steps to getting next one approved”: http://www.creditcards.com/credit-card-news/how-not-to-get-rejected-for-new-credit-card-1267.php
Also, make sure you are including all of your income: Alimony, child support, or separate maintenance income, odd jobs, etc! Every penny counts.
Maybe consider applying for a different secured card. I also recommend applying in person. My wife was offered a secured card the other day that she went to the bank.