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@Gordon
Thanks! Actually it's really helpful to have a decent size capacitor across the battery too. A smaller bypass cap is good, but an additional biggish (~10uF) capacitor across the battery could really help.
I'm not sure if it's just the internal resistance @rmd6502 mentions, but you get significantly less life out of a battery if you try and draw more than a milliamp or two. It's not really advertised very much but if you look at http://www.farnell.com/datasheets/1496885.pdf and the 'Load vs. Capacity' graph at the end, you'll see that with a 1k load (~3mA) you get 150mAh, but with 10k it's nearer 200.
It's not on the graph, but you can see that after 3mA the battery life falls off a cliff. Having a capacitor and then 'pulsing' the LEDs by multiplexing them/scanning them out means that hopefully you'll be drawing most of the peaks of current out of the capacitor, not the battery - giving you much better life.