When you close AceText by clicking the X button in the caption bar of AceText's window, or by pressing Alt+F4, AceText's window disappears. AceText itself continues running in the background. The icon in the system tray will remain visible, and hotkeys will continue to work.
To shut down AceText completely, right-click on AceText's icon next to the system clock, and select Shut Down AceText from the icon's menu. You can also select Shut Down AceText in the Collection menu of the main menu. AceText will then stop running.