In his dissertation, Rabbi Ezra Labaton has a lengthy discussion of the use of the term "sod" (actually 3 words in Arabic, in addition to the word "sod") by Rabbenu Avraham ben HaRambam. It seems very likely that this would be very similar if not identical to the usage of the Rambam. He writes (page 279):
Rabenu Abraham uses the problematic word “סוד” in a number of ways, some more specific than others. At times, the term has a definite connotation. If the issue at hand has a certain theological/ metaphysical thrust, or if it presents a psychological/spiritual aspect of the human drive toward perfection - issues which cannot be fully discussed in a written commentary as this - Rabenu Abraham terms the issue a “סוד.” [...]
In other instances, the term sod directs the reader to a more profound understanding of the verse which may be in addition to, or exclusive of, the peshat. Finally, sod is used, at times, in a more general way, indicating that there is some difficulty in the verse that has to be clarified or some contradiction that has to be resolved.
One example where Rabbenu Avraham uses the term to refer to a non-kabbalistic idea, is in Rabenu Avraham's commentary to Genesis (26:20) in which he writes:
יובן מזה סוד גדול כי האבות ע"ה עם כל עושרם הגדול ונכסיהם המרובים לא היו עסוקים בעניניהם הגשמיים ועסקם האמתי ובילוי זמנם והתעסקות מחשבתם היתה רק לרכוש ענינים רוחניים וכאשר התגלע ריב ועסק מן אותה הבאר קרא אותה (יצחק) עשק כלו' באר זו נתנה לנו עשק במה שאין בטבענו להעסק בו
It is understood from here a great deep secret that the forefathers with all their great wealth and their many possessions, did not really busy themselves with physical matters, but their true involvement and their time spent and their mental effort was only to acquire spiritual things. And when the quarrel erupted with the trouble from that well, he (Isaac) called it esek (trouble), i.e. “this well caused me trouble about that which I do not by nature become troubled (Trans. R. Labaton p. 269-9).