What I'd do is disable the automatic restart when you get a BSOD.
Here's how to do it.
Click on the Start button and then on Control Panel.
Tip: In a hurry? Type system in the search box after clicking Start. Choose System under the Control Panel heading in the list of results and then skip to Step 4.
Click on the System and Security link.
Note: If you're viewing the Small icons or Large icons view of Control Panel, you won't see this link. Simply double-click on the System icon and proceed to Step 4.
Click on the System link.
In the task pane on the left, click the Advanced system settings link.
Locate the Startup and Recovery section near the bottom of the window and click on the Settings button.
In the Startup and Recovery window, locate and uncheck the check box next to Automatically restart.
Click OK in the Startup and Recovery window.
Click OK in the System Properties window.
You can now close the System window.
From now on, when a problem causes a BSOD or another major error that halts the system, Windows 7 will not force a reboot. You'll have to reboot manually when an error appears.
This will enable you to take a note of any error messages that showed up.
What I'd try straight after this is to update your graphics drivers - it has helped on my PC in the past.