A sufficiently long spin decoherence time is of particular importance for logic gate operations in quantum computing. One promising scheme of logic gate operations is based on electrically gate-defined semiconductor double quantum dots (DQDs). However, recent experiments have shown that hyperfine interactions between electron and nuclear spins are a significant cause for electron spin decoherence. Here we study the two-electron spin relaxation time in a DQD due to the hyperfine interaction and the electron-phonon interaction, at various energy detunings (ε) and magnetic fields. In particular, we focus on two limits of interdot energy detunings, where the zero is set at the S(1,1)/S(0,2) degeneracy. For ε > 0, we investigate the spin blockade by evaluating the electron spin relaxation rate from low energy triplet states to the ground S(0,2) state. For ε < 0, we calculate the electron spin relaxation time at the S(1,1)-T₀ degeneracy to examine whether the ST₀ qubit has minimal leakage. Our results show that external magnetic fields can reduce the ST₀ current leakage in the low bias regions, and the spin blockade is sealed better in the bias region where the influence of excited states can be ignored.