So it looks something like the above? If you are positive that your system clock is accurate am/pm-wise and timezone-wise and that your computer is switched on at 3am (VirusScan wont switch it on or wake it from sleep to run) then I can only assume that your software is an older version - do you get it through your ISP by any chance?
The reason I ask is because the fix has gone out some time ago for this and the scheduled scan shouldn't delay more than about 20 minutes if the CPU is busy at the exact time.
Double-click the taskbar icon to open SecurityCenter and then click about and post the version of SecurityCenter.
Also check Control Panel > System and Maintenance > Power Options and make sure nothing in there switches off any part of the system after a period of time, hard drive for instance.
Meanwhile try running the Virtual Technician to see if it can automatically fix anything that may need fixing: http://mvt.mcafee.com/
If that fails to help Technical Support is your best bet and they are available 24/7 and it is free via phone or online chat - linked at the top of this page under Useful Links.
They can link up with your machine, with your permission of course, and troubleshoot.
By the way, I moved this to VirusScan as a more appropriate spot and to get better attention.