In Dead Rising for the Xbox 360, you can unlock an extra mode called Overtime Mode, which extends past the regular story mode.
I would suggest starting this mode directly after unlocking it, that way you keep all of your items. If this mode is started from the main menu, you will not keep the items you collected from the regular story mode.
To unlock Overtime Mode, you need to complete all cases in 72 hour mode, talk to Isabella at 10am on the 22nd, and get to the Helipad by noon on the 22nd as well.