depends on which beam you're referring to....
Resort: always opens up at 7 am, and closes at various times.
Express: 1 hour before to 90 minutes - 2 hours, after park closing.
Epcot: 1 hour before to 2 hours after later park closing. (If MK stays open later than Epcot, so will the Epcot monorail.)
If there is a MK EMH in the evening, then both the Epcot and Express Monorail will close 2 hours after their respective parks close (or the MK closes, if later). Resort will stay open 1-2 hours after EMH ends. (Latest up to 4 am, I have personally seen).