If the computer simply restarts without any error message then there is a problem with your hard drive.
Please check your hard drives with ScanDisk. Right mouse click on a drive letter in "My Computer" folder, select the Properties from pop-up menu, go to the Tools tab and click on "Check Now.." button. Do this with all your hard drives.
Also check the BIOS and Power Management settings and turn off any power safe options for all of your hard drives.
If ScanDisk doesn't help then please try to turn off the "Scan Several Folders Simultaneously" checkbox under the "Files Scan" options in the Advanced Settings Dialog. Registry Healer will use less resources while scanning hard disks.
Also, it is suggested to stop the phase 1 (scanning the registry) at about 100-200 found registry errors and wait for finishing the phase 2 (scanning disks for corrections). Less errors will take less time to scan the disks. You can do several such partial corrections to fix all registry errors.
Please also be sure that you close any other applications when you run Registry Healer. Scanning the registry and hard drives takes a lotof resources and CPU power.