I just called WDW and asked about this and this is what I was told:
The MK monorail begins @ 7:00am & the EPCOT one begins at 7:30am. All monorails runs until 1-1 1/2 hours after the last park closes (which is typically EPCOT, except for days that the MK is open past 9:30pm & holidays like Christmas & New Years where the MK, EPCOT & MGM are open late.
Hope this helps!