Diagnosis
This is usually a moisture problem. Either water has gotten inside the handle and is shorting the switch, or a tiny bit of water is trapped under the power button itself.
How to Fix It
First, take it off the charger. Remove the brush head. Hold the handle with the button facing down and give it a few firm flicks with your wrist, like you're shaking down an old thermometer. This can help dislodge water droplets from around the switch. Then, leave the brush off the charger in a dry, warm spot (like near a vent) for a couple of days to fully dry out internally. After that, try it again.
If That Didn't Work
The on/off switch mechanism itself might be failing mechanically. If it feels loose or mushy compared to before, the internal component may be broken. If it's under warranty, contact Oral-B. If not, it's likely time for a new handle.
Heads Up
Try to avoid storing the handle directly under a cabinet where condensation can drip onto it, and don't press the button while the head or handle is soaking wet.