OK technodudes and dudettes, solve this

The scenario seems simple... 

We have several smoke detectors.  They are designed to beep in one way when they detect smoke (continuous, persistent beeping) and in a different way when the batteries are low (5 or 6 single beeps with pauses in between). 

A few months ago one of the fire alarms started making the "batteries are low" beep randomly (i.e. at 3 in the morning).  I assumed the batteries were low and replaced the batteries (with name brand batteries) even though they'd been replaced only 4-5 months before.  Another smoke detector started doing the "batteries are low" beep, I replaced those batteries. 

Both smoke detectors continued doing the "batteries are low" beep at random intervals (every few days).  I assumed we'd gotten a bad batch of batteries and replaced both batteries with new, name brand batteries, fresh from the store.  The smoke detectors continued doing the "batteries are low" beep at random intervals.

I then concluded that the smoke detectors must have died of old age, so I replaced one of the smoke detectors with a new one and put a new battery in the replacement.  It proceeded to do the "batteries are low" beep at random intervals just as the others had.

I tried "max" quality batteries, the smoke detectors still do the "batteries are low" beep occasionally.  They test as functioning correctly and they go off appropriately when I broil something and the kitchen is smoky. 

At this point, the house has not burned down but the smoke detectors still do the "batteries are low" beep occasionally for no obvious reason.

Any ideas?