On my 10280 (200mAh) Key chain 6X build, I figure about 30 minutes or so...
But the 10440 is almost twice as long. I would hope it has at least twice the capacity if not more.
A FlexDrive/blu-ray/single battery build is interesting... when the battery begins to drop in voltage, it will need to draw even more current to 'boost' to the approximate 5 volts needed by the diode.
So the current draw will increase as the battery drains.
But these lithium batteries are impressive. The rule of thumb is a 1C max. charge rate, and a 2C discharge. (I believe) So if it is a 600mAh battery, you would want to keep it to 1.2 amps current draw. But a 1C draw, will be much better for the battery!
But I tested a green module with a tiny 10180 (90mAh), and it ran that thing, even though it took over 400mA's current draw!
Jay