Yes, there is a slight draw from the radio even with the key off, but not enough to kill a battery in a week. It becomes an issue when you store the bike for an extended period of time like storing for the winter. I've let my bike set for several weeks and it starts right up.
I would suggest pulling your battery, charge it up, and have it load tested. Most car parts stores will load test for free...
EDIT: I see you have a 2013 which will have the ISimple setup, and there was an issue with those, check with your dealer about that. Still have your battery checked out to rule out a weak battery.