Try opening it in "Safe Mode" and see if it works better in there. If so, then there is something on the phone that is the cause. Bad app, malware, virus, etc., which will have to be removed to get it to work correctly. However, if it happens in "Safe Mode" as well, then it is likely something in the "Settings" was changed. I would go in there and check the backlight timing to make sure it is set to a longer time frame.
To get into "Safe Mode" please do the following.
1. First turn off the phone.
2. Next press and hold "Power" until you see the manufacturers logo on the screen, then release the power button.
3. "Quickly" press "Volume Down" and hold it for few seconds until you see the message "Safe mode: ON" or something similar.
4. If you wanted disable it, simply repeat the steps above, and you should see "Safe Mode: OFF" rather than on.