Nei's game is simply very difficult. There's a particular trick to advancing beyond a certain point. You have to go through certain events in a specific order to trigger an event, in which Nei gets knocked out, to advance the game. It's not a bug in the remake, it's just tricky game design. This is in the original game, also.
I started writing a walkthrough for Nei's adventure a while back, but lost all my progress in a hard drive crash.

If I ever have time, I hope to restart it again at some point.