The story is about a man who slowly but gradually finds out that he is living in a virtual reality. Eventually they let him return to the real reality, but then, after a while he starts to notice things again that make him suspect that once more he's in a virtual reality.
It's a bit similar to what the Enterprise (TNG) crew did with holodeck character Moriarty, but that's not the story I mean. Also, if I remember correctly, the equipment is a bit similar to that in The Matrix.
I remember reading this story when on holiday in 1996 and the book was probably quite recent then. The copy I read was in English and I'm pretty sure the author is American.