The Ridvaz rejects this answer and instead says that the prohibition is only to return to Egypt with the intention of settling there. If, however, one travels there without the intention of staying but afterwards is prevented from leaving due to pressing circumstances (such as the services the Rambam rendered the king and the Jewish community) one has not actually transgressed this prohibition. [In fact, the Ridvaz himself lived in Egypt for a period of time where he established a Yeshiva.]

It is interesting to note, however, that the Kaftor Vaferach writes that the Rambam would sign his letters "the writer, who every day is guilty of transgressing three sins," referring to the three verses where we are enjoined not to live in Egypt. From this we see that despite the fact that the Rambam certainly had good reason for remaining in Egypt, it bothered him deeply.