Does the module have to stay plugged in?
Short answer
No. The module writes the change to your car's settings, so you unplug it afterwards and store it until you need it again.
An MWMods module is a programming device, not a box that has to stay in the car. It applies the new setting to the car's own control units through the OBD-II port. After that, the car keeps the setting by itself - for example a lower ride height, or a DYNAMIC SELECT program that is remembered after each start.
Keep the module in a safe place. You will need it if you want to change the setting again or return to the factory configuration.