I played the game on PS3 and believe I had a similar issue, but I ended up saving eventually and having no problems in the future.
Raiden III is kind of backwards, because instead of pressing X to accept, you press circle to accept (like Japanese import games), so that may be part of your problem (as to why it keeps asking for data save, and you keeping backing out causing the messagebox to pop up over and over again).
This is a question for the PS3 101 thread OP, just to let you know.