97 Altima electrical problem

The 97 Altima that has been my joy for 110k miles now has a problem. The car no longer gets driven much, maybe 3 times a week for a total of perhaps 30 miles. Still that should be sufficient to keep the battery charged, right?
The battery does drain, however, in 5-6 weeks; I have to recharge it and all is well for a month or so.
It has never had a starting problem... I've had the battery checked and I checked that the alternator (near new) puts out 14 volts at idle.
With the battery removed I checked the electrical resistance across the terminals and measured 1100 Ohms. I suspect it should be more... so I'm guessing one of the circuits is slowly draining my battery.
Can I get some guidance?