This question is mentioned on the Fantom page:
http://fantomvacuums.net/faq/faq.shtml
and is raised in numerous forums. The answer on the Fantom page re being caused by "turning the roller by hand" is completely bogus. There is indeed a circuit board you can see by going through the belt replacement procedure detailed above. The circuit board has a switch on it that is designed to turn the brush motor off when the vac handle is upright.
There are several things that can cause the problem. The brush is intermittent because either the switch on the board has gone out (caused by manufacturer using a cheap switch) or by wear on the switch roller and the vacuum (caused by poor design and manufacture), or because the board has moved, causing the switch to not be depressed fully. The board with the switch is held in place by just one small screw in the center. This allows the board to pivot around the screw so that when the handle goes up and down, it doesn't press the switch far enough to fully turn it on. When you remove the front cover per belt replacement, you can see the switch and move the handle up and down to determine whether the handle on your vac is properly depressing the switch. It should make a good solid click.
This seems to be almost a universal problem that renders the vacuums unusable after a few years. If the switch is OK, but not being depressed fully due to wear or board movement, then you can fix it mechanically by tying it in the on position with something like a wire tie. If the switch itself is bad, then you'll need soldering skills to fix it. If you have those skills, you can figure out what you need to do. Tying the switch in the on position worked for me. Just be sure you turn the beater off with the switch if you're using it in the upright position on carpet.
Its a shame these vacs have this issue, because it is otherwise a nice vac with a nice ergonomic design, but the foot latch that holds it upright chronically breaks off, and the brush motor chronically has this intermittent power issue. It seems that Fantom is being intentionally evasive about the solution, because once you know what the problem is, you can see that it is the result of a bad design. I have a Hoover that is 30 years old - it does a very mediocre job at cleaning, but it still works great and nothing is broken off it. Why is it so hard to make a decent vacuum cleaner??
Steve Rogers, October 2006