I understand how everything can come to a halt when the vacuum shuts down. It sounds like you have done a good job checking for the most common causes. I see you removed the power mate and checked the hose for suction. If there is an airflow problem which would mean that there may be a partial blockage in the airflow, it may still be in the hose.
Take the hose loose from the canister to see if it still comes on. If it does, then I would check the hose and wands all the way down to the power mate for any obstruction.
If the motor is running and there is no suction, try pulling the dust bag out and briefly running the vacuum cleaner without the dust bag to see if it will pull any suction through the hose. If it gets suction without the bag then the motor may need to be replaced. This type of repair would likely need to be completed by a service technician.
Since both the check bag indicator and the reset stay lit, if the above checks do not produce results, I would suspect a loose or bad belt.
Remember to disconnect power to the vacuum before attempting service or repair
The image below will help access and replace the belt if necessary. If a new belt is needed, you can order here;
Sears Parts Direct
If the belt checks out, the wiring in the hose needs to be checked as well as the PCB board and the motor. The motor may be failing even though it is running. The image to help with hose wiring checks and repair is below. If you do not feel comfortable with further checks, you can schedule a Sears technician here;
Sears Home Services
I hope this information helps. If further assistance is needed, please reply. Thank you for using Manage My Life.