You can apply to a blogring as many times as you would like! 

However since the same leader will view your application, your odds of getting approved a second time probably won't change unless you put more time into your application.  You could also try contacting the leader through email, and asking why you were disapproved.

If you'd like to apply to the blogring again, please see:

How do I apply to a blogring?
http://help.xanga.com/howapply.htm