This is not something that we can address in the app. Why would it automatically continue on if something on the hardware had stopped it? Kind of defeats the purpose...
As you found you can continue the flight by instructing the aircraft to move on. You can also handle this by pausing the mission and then pressing Continue (hey, look, it is handled in the app! We aren't shameful! Yay!)
You did not provide the Map Pilot log file which is what would actually tell what caused the aircraft to stop so we provided multiple links to cover multiple cases. By the time the data gets uploaded to AirData and displayed using the public links the important information has been stripped out.
When the aircraft stops, the pilot in charge should identify the cause using the Aircraft Errors screen and make a decision on whether it is safe to more forward with the flight or not.
For most mapping flights, it is safe to operate without the Obstacle Avoidance system turned on since you are flying high. Such settings would keep these annoying stoppages from occurring if that was indeed the problem.