I don't have a battery installed right now because they only last a couple of days
It would be interesting to see how long a battery would last if you clipped one of the leads to the capacitor as Dan suggested.
Well in the interest of experimentation, I just cut one of the leads and dropped in a new battery; I did read on another forum that this prevented the battery from draining as quickly, so my fingers are crossed. It would be nice if this worked, then my station (and others in the future) wouldn't be down while waiting for parts.
FYI, it has been over a week since I clipped one lead, and I haven't had a problem since. It appears that when the supercap fails but remains connected, it sucks the battery dry. Based on Davis' claim of 8 months with no sunlight, I would have to guess one could operate like this for at least a year if the solar panels get normal sun during the day.