Sony VAIO shuts off constantly.

Hi and Welcome to the forum

This could be a whole raft of things from the simple to fix to a major hardware failure, but lets start with the smiple things that I am thinking of at preset.

1. Is the laptop cooling grills clean from dust? as one of the major things that can cause a PC to randomly turn off is heat and a build up of dust will cause components to heat up and fail, now what you can try is to use a hoover to suck out any dust to getting some air in a can and blowing any dust out.

Make sure the laptop is on a clean flat surface and not on a lap or materials that will block the air vents/grills.

2. Do you have the same issue when the laptop is on mains only (no battery in) or when on battery or with the battery in?

Try if not already taking the battery out and plugging into the mains, this may rule out a failing battery as its now 4yrs old, unless you have purchased any new ones in that period.

3. Boot into safe mode (F8 at boot and choose Safe Mode with Networking) while this is a longer shot as you have re-formatted and re-installed Windows its a useful test to do, just in case one of the 3rd party applications you have is causing this, reason for suggesting is we all have our favoured apps, be that security, graphics etc so even when changing Windows OS we put back these apps.