I think that what's happening has to do w/ the drop-out voltage of the linear regulator. I don't remember the series number for the regulator (LM318 or something), but there is an "over-head" in the regulator that essentially subtracts from the battery voltage even before it starts its current limiting. As a bad "fer instance", if you have a LR w/ a 2.5 volt drop-out, you need to have a voltage source that is a minimum of your desired voltage plus 2.5v. At 4 ot 5 volts, you probably aren't getting the linear regulator to do ANYthing. At 9 volts, it scoops its drop-out voltage off the top, and then regulates the remaining voltage.
LRs are NOT very efficient vehicles... Their efficiency rises SLIGHTLY as the source voltage gets closer to the target voltage, but still, the efficiency is around 50% (from hazy memory). With a LDO (low drop-out) regulator, you might have a drop-out voltage on the order of less than 1 v (some, now, down to a few hundred millivolts) which let you exhaust your battery a bit more, but don't to much at all for the efficiency.
Now... step-down SWITCHING regulators at, say, 90% efficiency... THAT's another story. ;-)
(for THAT story, read "9v x 595 mAh = 5355 mWh, x 90% = 4820 mWh / (3.6v x 20 mA) = 67 hours"? I've got to check my math on that...
that can't be right. Or maybe it can. Anybody else figure it the same way?
Ah... one thing, that's a the "optimum" current of 20 mA, not the 96 mA that the PAL uses... heh heh heh.
Sorry. Been a while since EE school.)