DIAGNOSIS: The metal drive shaft that holds the brush head has likely become loose or the retaining ring inside the handle has worn out. This is a common wear point.
FIX: First, ensure you're using a genuine Oral-B brush head (like the CrossAction or FlossAction). Knock-off heads often fit poorly. Push the brush head on FIRMLY until you hear a distinct click. If it still wobbles, the issue is with the handle.
IF THAT DIDN'T WORK: Look inside the handle's brush head socket. If the small, black rubber O-ring inside is torn or missing, that's the culprit. You can sometimes find replacement O-ring kits online, but it's often a sign the handle is nearing end-of-life.
HEADS UP: Don't use excessive force when attaching the head. A proper click is enough. Continuous wobbling will wear down the mechanism faster and reduce cleaning effectiveness.