Consider one observer at the center of the Earth and another at the surface, in a sealed box. Is the one on the surface accelerating? According to his measurements--remember, he can't see his surroundings, so he measures his acceleration with a scale--he is (c.f. the equivalence principle). According to the observer at the center of the Earth, he is not.
Why doesn't SRT apply to accelerated frames?
I assume you mean an accelerating frame. Frames by construction don't accelerate; they refer to inertial rest. SR does apply to accelerated frames (i.e., frames at different velocities). But what you want to know is, is there a principle of relativity that relates observers under arbitrary acceleration? Yes, it's called the General Theory of Relativity.