battery management IC - duracell alkaline
In the data sheet of the MAX6775, the device itself draws 3-7 uA, plus your voltage divider for the LBI input.  The input has very low (5 nA) LBI bias current, so you could get away with some very high-valued resistors for your divider (for reference, if you have 5 nA bias, you would still be ~1% accurate with a divider that draws 500 nA, or 0.5uA, adding little to the chip itself.)  And in the 5 uA range for the monitor circuit, the time it would take for your circuit to discharge the batteries would be on the same order as the self-discharge/shelf-life of the batteries themselves (using AA's for example, and assuming we aren't talking coin cells, but you didn't specify).

If you need to get it lower, you could use a high-side MOSFET to disconnect the battery monitor from the batteries, but then again, your micro is likely going to be drawing several microamps of its own in sleep at the very least.