No need for that attitude man. If you don't enjoy the discussion, you don't have to participate.
PaulRB, et al.,
Looks like you are correct. The output voltage seemed sufficient (measured to be approx. 6.01 volts, two in series), but I couldn't tell how much capacity it had at the time. I was tinkering and even though they were relatively new batteries, I swapped them out for another pair of new batteries, and it worked!
Also, I didn't think the estimated mAh accounted for voltage drop over time, so in the new set of batteries, I let it run. After 10-15 minutes, I noticed that the LEDs no longer lights up, and it would reset on its own (confirming exactly what you suspected). Turning it off for sometime, then back on seems revive it and allow LEDs to light up as expected again. Not sure how long I can cycle it for but I only need it to operate for <2 minutes for my project, so this is sufficient! Could be a good data point for other folks if they have similar needs.
Out of curiosity, could I, theoretically, delay the voltage drop by adding another battery in series? In other words, would a series of 3 batteries technically run longer before the arduino begins resetting? Or would the internal resistance add up, thereby negating the extra voltage gain? I don't actually have the volume for it, but if it helps, I would consider it in my next revision (or perhaps with lithium batteries! 
).