To do this you must set Options > Sessions > Save Session on close. The recommended setting is Prompt to Save.
When you do this, you will get the following prompt when you close AQT.
To see the Full Save Dialog, either:
Auto-Saved Sessions are saved with a name starting with $.
You can save your session at any time with (from the Database Explorer window) File > Session > Save Session.
Unless you are saving your session permanently:
Manually saving your sessions is useful in the following circumstances
AQT has an option automatiically save your AQT session. This can be activated with Options > Sessions > Automatically Save Session.
When this option is selected, AQT will save the state of your session while AQT is running. Your AQT session will be saved in the case of an unexpected termination of AQT.
This is very resource intensive as AQT will write the state of your session to disk on a continual basis. As a result, this option should only be used in rare circumstances.