How do I keep a meeting open on Adobe Connect continuously?

If you have the Named Organizer license, then the member of the Meeting Host group must be in the room and active. Active meaning that that user is focused on the room and the mouse is moving. I recall that Connect will close a room without activity for ~6-8 hours.

If you have the Concurrent User license, then anyone can come and go from a Meeting as needed.

The Named Organizer licensing is a license for an individual to run a meeting, where the Concurrent User license is a license for individuals to be in meetings.