Running an RX and a couple of standard servos should normally be perfectly OK off a set of AA duracells, assuming that all the components are in working order. The problems start when the current draw increases.
The servo works by taking the length of time that the control pulse is on and turning it into a voltage. This is compared with the voltage taken from its position sensing pot. If there is a difference, the motor drives the position sensing pot to a matching position, at the same time turning the horn, and stops.
This derived reference voltage is a percentage of the servo supply voltage. If this is caused to vary, the servo will try to drive. This will put a load onto the supply voltage and cause a variation which will be seen as a demand to re-position. Just one tiny twitch can start the thing interacting.
If the RX pack is supplying everything, use NiMH rechargeables. Their voltage is less liable to sudden fluctuation. At the same time, check out the lead resistance. This can have the same adverse effect, for the same reason.