Click on the series of icons located in the bottom right corner of the screen
Select the Gear icon from the menu that should pop up
Make sure you have selected the “Network” page once you are in settings
Once you have connected to your desired network, make sure that the toggles (circled in red to the left) are set to ON.
Your settings should save automatically so you are safe to close the window
This should help if the Chromebook continually requires a network password from a known network.