It might depend on the type of battery you are using.  If you're using
a battery technology with a steady downward ramp in output voltage (ie
carbon/zinc), there may be significant engery remaining in the battery
AFTER the voltage drops below that which will allow a linear regulator
to operate your equipment.  Some of the switchers are starting to publish
boost/buck designs that provide correct output voltage with input ranges
from below to above the target voltage.  After all, you're not really
optimizing for current, you're optimizing for batery life...

BillW