The buttons are made to make a display go dark if you hit them while the display is lit. so that part is normal. The fact that they won't turn back on still sounds like a button problem.
To test for software, which is much less likely, you can try starting up the device in "Safe Mode" and see if you have display not turning back on after pushing the buttons problem in there or not. If you do have it, then the problem is hardware. If you don't, then something running on the device is the problem. Virus, malware, bad app, etc.
To get into "Safe Mode" please do the following.
1. First turn off the tablet.
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.
If it is the button, then it will need to be repaired.