The motor support ring is a bracket and flange combination which connects the downrod support, fan motor, and motor housing together in the center of the top housing plate. This piece is responsible for supporting the entirety of the fan below the downrod.
Unfortunately, for reasons unknown, it is composed of a lightweight plastic which becomes brittle and cracks with age. Most often the flange portion (where the downrod screws) is where cracks occur, because of the tension of the set screw on the downrod. The set screw tightens the support ring against the downrod preventing the entire motor assembly from unscrewing, especially during operation.
Tension on the set screw and therefore on the increasingly brittle support ring is greatest when there is significant torque on the downrod, which is most commonly when the motor is activated on high speed from a still/off position.
This ring supports the entire fan motor assembly, blades included. Cracks in the ring could result in the motor assembly no longer being connected to the downrod, and falling. Stripped threads could result in the fan unscrewing from the downrod.
Assuming you have one of these fans, and therefore the plastic ring:
1. Inspect the ring for any cracks, or any stripping in the threads of the downrod flange or the set screw socket. If any such damage is present the fan should be removed immediately.
2. Be sure the set screw is not overtightened. It should be secure enough so that the motor assembly cannot be unscrewed from the downrod, and no tighter.
3. Use caution when activating the fan, especially on high speed. Theoretically the fan should not be used at all.
Unfortunately no replacement parts are currently available for this ring. Supposedly other fans made in the same era have used a similar part, of metal construction, that could be retrofitted. The ornate brass fan in the gallery features such a replacement ring. The availability of such compatible fans or any spare rings is doubtful; I myself have not come across any. Hopefully in the near future replacement parts will be available, this is more likely if there is a demand for it other than myself.