Electrolux Vacuum Cleaner Epic series 3500SR: The motor runs but not at full power and then quits then will start again.

Check the piece of flex hose between the vacuum body and the power nozzle. This will sometimes get a blockage in it, causing varying motor speeds.
You can remove the tube by grasping it firmly and pulling from the power nozzle. Then twist clockwise to remove it from the vacuum body. Clear blockage with a wooden spoon handle or similar blunt object. Insert tube into body and twist counter-clockwise until tight. Insert other end into power nozzle about an inch, or until it stops.

Another thing to check is the foam filter at the bottom of the bag well. Remove and replace if necessary. If a new one is unavailable, the vacuum can be used until you get a new one. Or rinse the old one out and allow to thorougly air dry before using. Also check the screen covering the motor intake and clean if needed.

Also, if your machine is fitted with a afterfilter on the lower side of the tank, this may need to be removed if dirty.

There are a couple of possible reasons that are causing this issue
1. A blockage can cause lack of power, but it wouldn't cause your vacuum to turn off. So I don't believe you have a blockage.

2. An electrical short could be present. If the vacuum goes to full power and fades down and stops, this is a symptom of an electrical short. But, I don't believe this is your issue.

3. Worn/Stuck Armature Brushes in motor. This is what it sounds like is wrong with the vacuum. Armature carbon brushes are what create the electrical contact on the armature in the motor. When they wear down, it causes the vacuum to run under powered and will either run until it loses contact with the brushes on the armature.

Tools required
Long Phillips Head Screw Driver

Now how to disassemble the vacuum
Unplug the vacuum from the power outlet
Remove the one screw on the back off the handle located on the carrying handle
Remove Handle
Open bag chamber and remove bag
When looking down bag chamber, remove foam motor filter if present
Remove two screws inside bag chamber. Located in front left and front right corner
Remove the two screws on the rear outside of the vacuum by the bottom cord wrap
Once all 4 base screws are removed lift hold onto bag chamber and lift off bag chamber about 6 inches
When the base and bag chamber separate, you will see under the bag chamber that there are two wires you have to disconnect from the bag switch
Remove those two wires from the bag switch
Now you can completely remove the bag chamber off the base
You should see the motor.
Lift the motor out of base
There will be two wires on each side of the motor
Disconnect those two wires
Locate the Carbon Motor Brushes
Depending on what generation of Discovery, Genesis, Epic there will be screws to release these brushes
Once you remove the brushes you can now inspect the brushes.
When they are removed they should had at least 3cm of brush, if not you need to replace these brushes. They can be found at most vacuum repair shops as they're a common part.
If these brushes were stuck, push in and out of housing and to free them up.
Once you repair your brushes, be careful when inserting the motor back into the housing. There is a rubber grommet that sits at the base and the base of the motor, be sure to have this in correctly or you motor will not be sitting correctly. If this happens your vacuum will not go back together correctly and you will have weak suction.

Once you make sure the rubber grommet is correctly installed, reverse your steps and your vacuum should run as normal!