On Wed, 20 Nov 2013 06:04:17 -0800, wrote:

That it runs once a week is not a sign of the generator
being dumb. I still bet that it runs once a week as a
self-diagnostic, not to charge the battery.
What yours exactly does, none of us here know.

TO lay this one to rest, I snapped a picture of the placard
on the generator next to the control panel:
http://farm3.staticflickr.com/2880/1...d40085a1_o.gif

SET EXERCISE TIME INSTRUCTIONS
Place Manual/Auto Off switch to "Off" position.
Place and hold "Set Exercise Time" switch to "On" postion for 5 seconds.
Wait 30 Seconds.
Place Manual/Auto/Off switch to the "auto" position.
Failure to wait 30 sec. may cause engine to start.
If engine does start, it will shut off automatically within 2 min.
Generator will now exercise every 7 days, at set time.