Bots now have to respond to users within 24 hours of their initiating a conversation. If for some reason it takes longer to formulate an answer, bots are granted permission to send one message outside of that time frame—but no more than that. From Facebook's blog post:
Bots will not technically be able to message users more than once beyond the 24-hour window (message will not be sent). During the transition period for existing bots, these messages will go through but will be flagged if found.
When it comes to opt-in subscription messaging—which Facebook is still testing—bots can contact users at any time, but they cannot send promotional messages. Only the following use cases qualify for subscription messaging:
News: Bots whose primary purpose is to inform people about recent or important events or information in categories such as sports, finance, business, real estate, weather, traffic, politics, and entertainment.
Productivity: Bots whose primary purpose is to enable people to manage their personal productivity with tasks such as managing calendar events, receiving reminders, and paying bills.
Personal trackers: Bots that enable people to receive and monitor information about themselves in categories such as fitness, health, wellness, and finance.