It would help if you could read what the BSOD is saying before it disappears. You can set the machine NOT to reboot at a blue screen. In which case you would have to turn it off manually in order to reboot.
Right-click Computer and select Properties.
Select Advanced System Settings
Select Settings under Startup and Recovery
Uncheck "Automatically Restart" and OK it.
Next time it happens the BSOD will stay on the screen and you could note the error code.
BSOD's are usually cause by hardware failure, although they can be software-related.
Windows Event Viewer might be able to give you a clue.
Go to Start/All Programs/Administrative Tools/Event Viewer - it takes a while to initialize
Then click Custom Views to expand the tree on the left and select Administrative Events and see if anything is there from the time of the crash.
Alternatively expand the Windows Logs and check each header there for clues.
If there is anything noted please post it here. You can copy most entries as text using the righ-hand menu.
One thing you could try is checking the hard drive for read errors.
Go to Start and type into the Search Programs and Files box "cmd" (minus the "")
In the choices above you will see cmd.exe or just plain cmd - right-click that and select "Run as Administrator".
In the subsequent Command Prompt window type in chkdsk /r (with the space between k and /) and hit the Enter key
If you have more than one partition you can specify the drive letter like this: chkdsk C: /r (with spaces between k and C, : and / & where C is the drive letter - change if applicable) and click Enter
You will get an error stating that the volume is in use and to start at next reboot Y/N?
Type in Y and click Enter.
Type in Exit and reboot and let the utility check the disk for errors.
See if that helps.
An afterthought and as a supplement to what I already stated; this could be a case of overheating. When VirusScan is running is it possible that something else is running too? Or is it possible that fans are clogged with dust perhaps or not performing properly?
When VirusScan is running do a Ctrl -Alt-Delete to call up Task Manager and check the Performance tab to see if the CPU shows high usage..
It would help if you posted your computer details - CPU, RAM and free HDD space.
By the way, any idea exactly which file it stalls at?