Ok, I tried to use 4x AA batteries to drive three servos at the same time and it worked! The problem was low signal voltage I guess. The servo specs said they were for 4.8-6V, and the regulator gave steady 4.97V that I used to power all the servos. The funny thing is that I could run three Futaba S3003 servos @5V without problems.
It's not about the voltage directly, but rather the current demand that the servos are drawing. Servo companies do a poor job of listing the maximum current they require and each brand and model of servo will consume a different amount and of course the mechanical load placed on the servos will drastically increase their current consumption. If you try and draw too much current from a voltage regulator it's output voltage will sag or even shutoff. So yes most hobby servos will work just fine with a steady 4.8 to 6vdc DC voltage, however the source of that voltage must be able to handle the peak current requirements of all the servos it is trying to power. I usually recommend that the DC power source be able to handle at least 1 amp per servo attached if you want to avoid voltage dips, board resets and other annoying problems that servos can bring to the party.
Lefty