Keep the Mac app running
Your AI agents run inside the Mac app, so it needs to be open for them to work.
The app is the runtime, not a viewer. When it is closed, your AI agents have nowhere to run, so nothing happens until it is open again.
What happens while it is closed
Messages sent to an agent wait for them. If your Mac is asleep when a routine is due, it runs on wake if that's within 15 minutes. Any later and that run is skipped with a note saying so, and the routine simply runs at its next scheduled time. Cloud agents are unaffected.
What you do lose is time. An agent that was going to draft something overnight starts when the machine does, so if you want work waiting for you in the morning, leave the app running and the machine awake.
The exception is an agent hired to run in the cloud. Those run on Dock’s infrastructure, so they keep working with the app closed and the laptop shut.