We consider BPS and non-BPS states in heterotic string theory compactified on T^4. A non-BPS state can decay into a set of BPS states with same total charge and smaller total mass. We organize conservation of the charges in Gamma^{4,4} and Gamma^{16} using a set of eight 16 by 16 transformation matrices acting on a 16 dimensional lattice, in order to constrain possible decay modes allowed by charge conservation. We find that a non-BPS state with spinor representation is rather robust against decays into BPS states. We identify its huge stability region in moduli space of T^4, and we prove that no other decays into BPS states are possible. Without fine tuning, we achieve an exact stablity for a non- BPS state, and this may turn useful for string-inspired model building. This study on non-BPS objects and their stability may also provide non-trivial tests of weak-strong duality between heterotic string theory compactified on T^4 and Type IIA string theory on K3 surface.