"Safe Mode" shouldn't keep the phone from turning off. So you know.
If the "Safe Mode" is still running after you restart your phone(or can't restart the phone), I would then check to make sure your "Volume Down" button is not stuck. Check to see if it has anything stuck in it as well, dust, etc. Anything like this can cause the phone to go into, and get stuck in, "Safe Mode".
If that doesn't work try this...
Use the "Status Bar" to turn off "Safe Mode'. Pull down (swipe) the "Status Bar" of your phone. Now tap the "Safe Mode" button. This should turn "Safe Mode" off. Now your phone will automatically restart, so that it boots up out of "Safe Mode".
If you want to get rid of/disable "Safe Mode".
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: OFF" or something similar.
4. If you wanted re-enable it, simply repeat the steps above, and you should see "Safe mode: ON" rather than off.