Overclocking my toothbrush

Have you tried using a normal recharegable AAA battey?

They're only 1.2v, but they have a lower internal resistance, so it might make up the difference. It's worth a try.

You are more than doubling the source voltage to the motor. TBH I doubt the motor can handle it, the brushes are probably dying. If you do add a resistor, the speed of the vibration will be reduced (which I presume you don't want). If you are open to the idea of a lower speed, add a resistor in series and vary this resistor's value till the speed is what you want. Now check if the motor lasts longer. I can't help in any other way because I have no clue where the fault it.

I'm guessing, but the significantly higher voltage is making the motor run too hot. It sounds like the bearings are ceasing up when hot. They might be getting significantly hot even if the overall unit is just unusually warm. The heat can hurt the lubricant, and differential thermal exapansion of different materials can make them bind.

Overdriving a motor by this amount is not a good idea. Remember that this is a high volume consumer product, so I'm sure significant engineering effort went into reducing cost so that everything is designed to work just within its limits.