Maybe you should buy one and then you would know the answer to your question :-)
The power does not come from the mud or vegetables it comes from the "battery" that is supplied with the clock in the form of specially treated zinc and copper electrodes. The mud acts as a salt bridge to complete the construction of the battery.
In time this battery will wear out and will stop working like all batteries. And I'm afraid to say that like all batteries it takes more energy to make them at the factory than you will ever get out of them.
Take a read here:
http://en.wikipedia.org/wiki/Lemon_battery