How big is the plane? 140-150cm span? And weight? If you press hard on the elevator...does it flex? Flex in the elevator could induce flutter in the stab.
As speed suggested...I also would cover the stab with 1,5mm balsa on both top and bottom.
I have many times seen flutter occur in both sport and pylon racers and every time it has been due to a too weak stab or if on a wing, having the ailerons go out all the way to the tip of the wing and being to flimsy.
A too short elevator arm could also be the culprit in conjunction with flex in the elevator push rod or linkages. I do recommend using either wires or using a carbon rod for elevator control.
On my airplanes both sport and pylon racers I strive for having as short servo arm as possible and as long elevator arm mas possible and using 100% or more throw in the transmitter, this to reduce play in the gear train in the servos.