When you get your 'stopover' (referred to in the real world as technical stops generally used for crew rest and/or refuelling) then stop MyAAS and save the flight as a refuelling stop, you will see the option. Close your flight and have a break.
When you're ready to set off again, start Flightsim and just before you push back, start MyAAS and you will see your flight in the queue. Simply open that flight and resume.
The 50 minutes ground time is cumulative for the whole flight so this is in effect the taxi time for each sector in the flight. It's anytime that the gear has pressure on them so be very careful to manage this properly. If you exceed your ground time you flight will not be uploaded. If you do three flights in the leg, you only have about 15 minutes total ground time at each airport, both after landing and before takeoff so you MUST remember to close and save MyAAS.
I will try to get some screenshots on one of my flights to show you what to do, unless Joe has some somewhere. It is explained at
viewtopic.php?f=51&t=7007