Although it's a pain, laptops are such proprietary devices that issues with them should first be directed to the manufacturers customer support services. The usual things would be to try and determine if this has always been a problem and, if not, when did it start? If it's a recent problem, can you point to something you may have done or changed about that time....driver updates, software installations? Then, are you sure you are pest free and hardware drivers current. This is because the shutdown/restart process is quite different from program launching and terminating. There is a lot of hardware interaction that occurs, closing of programs and services, etc. You might want to try Sony if you cannot find a definative answer here.
Many of these comments discuss a problem of continually rebooting. My problem is the opposite. Most of the time but not all when I want the computer (Vaio GX550 laptop) to reboot it shuts down and I have to restart. Any suggestions?