|MadSci Network: Chemistry|
Without a more detailed description it's hard to do more than suggest things. My initial suspicion is that leaving the electrodes in the potato has corroded the zinc and tarnished the copper; in both cases, you build up an insulating layer on the electrode surface.
Another of our moderators suggests that refrigerating the potato might help; perhaps it's lost some water to the air.
On the other hand, the Edmund Scientifics Potato Clock runs for quite some time. But that might be due to the fact that electricity is always flowing--therefore you don't get a buildup of insulating junk at the electrode surface, because it moves away as part of the current flow.
I suggest that you remove the electrodes when you're not drawing current from your device. Perhaps storing the potato in a plastic bag in the refrigerator would also help.
Try the links in the MadSci Library for more information on Chemistry.