A persistent spin helix (PSH) in spin-orbit-coupled two-dimensional electron systems was recently predicted to exist in two cases: [001] quantum wells (QWs) with equal coupling strengths of the Rashba and the Dresselhaus interactions (RD), and Dresselhaus-only [110] QWs. Here we present supporting results and further investigations, using our previous results [Phys. Rev. B 72, 153305 (2005)]. Refined PSH patterns for both RD [001] and Dresselhaus [110] QWs are shown, such that the feature of the helix is clearly seen. We also discuss the time dependence of spin to reexamine the origin of the predicted persistence of the PSH. For the RD [001] case, we further take into account the random Rashba effect, which is much more realistic than the constant Rashba model. The distorted PSH pattern thus obtained suggests that such a PSH may be more observable in the Dresselhaus [110] QWs, if the dopants cannot be regularly enough distributed.