I have recently purchased and assembled a Tiny Circuit Tiny Saber.  I love it, but its battery doesn't seem to hold on to a charge very long.  I charge it and put it away for a day, when i come back to it the following day it's discharged.  I'm sure I left it powered off, and this has happened for the past few days.  Is this expected behavior due to the ultra bright LEDs?

If the battery is plugged in then it's always drawing power.  Even if the saber is in "Sleep" mode with no LEDs showing, the program is still looking at the touch sensor and accelerometer, waiting for some input.  It will eventually run down.

If you incorporate a switch into the system to isolate the battery it should keep its charge and the board will be truly powered off.