In our minds, we are talking about 11:59 PM at UVA, which means the Eastern time zone. The Common App accounts for the time zone of all applicants, so those of you out West won't see the app shut down at 8:59 PM in your time zone.
We DO NOT recommend waiting until the last few hours to submit your application. The Common App team stays up all night on deadline nights, but you can't expect instant help if something goes wrong with submission since there are apt to be scores of students submitting requests for help.
Good luck to those putting the finishing touches on an application!