There are different situations that pause and resume the bot.
Pause bot action
You can add a Pause bot action within a flow to pause the bot. Whenever the action is called the bot will stop responding immediately.
Using the plugin
The most obvious one is using the Flow.ai Front plugin and manually resuming or pausing by pressing the pause or resume button.
A bot will automatically resume it's operation whenever an agent triggers a bot event using the plugin.
By default Flow.ai will resume the bot after a number of minutes no more interactions has taken place. You can configure this within the Flow.ai Brain settings screen.
Another event that will cause the bot to pause is when a human agent sends a reply using Front. The bot will automatically resume after the auto resume time period has passed.
Resume on archive or delete
Whenever a conversation is archived or deleted within Front, either manually our using a rule, the bot will resume responding to a customer.
Make sure you have the webhook rule configured to watch all inboxes that are used to archive.