Here are some scenarios that will cause an Import from the FamilySearch Family Tree to stop. Also notes is if the Import can be resumed where it left off.
1. User clicks Cancel on the Import and it will stop - you can not resume the import where it left off
2. Sometime FamilySearch will log you out and RM will attempt to login again. As long as FamilySearch did not loose the session call it will resume the import where it left off.
3. FamilySearch website goes down (due to maintenance or updates) - connection is severed - import cannot be resumed
4. Your Internet Provider temporarily shut down or interrupts your connection - import cannot be resumed.
5. Your computer goes to sleep or hibernates during the import. This should sever the connection and stop the import so it cannot be resumed.
As long as your Import session is not disconnected from the user or FamilySearch end it should continue to run and complete. If your settings were for more generations than what is on Family Tree it will not effect the import. It will simply import until the line is exhausted.
Right now FamilySearch is not throttling the download connect speed through the FT API. They have informed us they will start doing so in the near future. The import speeds and stats people see today will be changing.