When the screen blacks out, shine a torch at an angle close to the screen to see if you can detect if a display is still there. It will be dim but a darkened room will help.
If you can see the display you most probably have a backlight problem.
This can be caused by (depending on laptop model, you didn't say what model you have) a faulty backlight power inverter, faulty backlight power cable, faulty lid switch, faulty video cable or faulty screen.
If you cannot see the display with a torch, connect an external monitor to the laptop and check its' display when the laptop's screen blacks out.
If the external monitor display stays on, then you either have a faulty video cable, faulty video cable connections at either end (motherboard or screen) or a faulty screen.
If the external monitor display also turns off then you have a faulty GPU or motherboard (which is basically the same thing as the GPU most probably is mounted directly onto the motherboard.
If you can still 'see' the display when the screen goes black it indicates that there is a problem with either the voltage level of the power supply to the backlighting going intermittently faulty or that somehow the connections supplying the power are going more resistive (as best as I can determine the power from the backlighting is supplied from the motherboard and not a separate inverter board in the laptop).
Just wondering if it could perhaps also be a problem with the software control of the backlighting. When the screen dims have you tried pressing Fn + F6 together to see if you can increase the brightness at all?(Fn + F5 dims the screen)
Here is a link to a webpage that shows how to dis-assemble the laptop. It may help if you wish to see if there is anything obvious such as a loose video cable connection etc on the motherboard Unfortunately it doesn't show how to dis-assemble the lid to view the screen end.
As I cannot find a service manual online, without a schematic diagram it will be difficult to ascertain where exactly the problem is. It may be that you will have to contact a reputable, professional laptop repair service and ask for a quote to repair the laptop