Most of the time, if you have a chromebook that has random shutdowns, restarts, logouts, etc. it is usually due to plug-ins that are installed on the chromebook. This usually happens under the student login, therefore, you may need to do the steps below. 

If these steps do not work, and you have also tried to reinstall the OS via chromebook recovery utility  , please send the chromebook to the I.T department as we can send them out under warranty. Here are the steps:

  1. Login with your google staff account
  2. Click the status area, where your account picture appears.
  3. Click Settings Settings and then About Chrome OS.
  4. In the "About" window that appears, click Check for and apply updates. Your Chromebook will start to install any available updates.
  5. After the updates are installed, click Restart to update.