When I take a portrait with settings which result in a DOF shallow enough that the subjects' movements risk missing focus on the eyes, should I use continuous AF mode - is the continuous AF fast enough to compensate little movements of the model/photographer or should I stick with the AF-S mode?
With a depth of field of 3 cm/1+ inch, there isn't much room for error. Since you say you're shooting a portrait I'll assume this is a portrait of a person and not a static subject. (If it were a static subject, though, I would tell you to lock the camera down on a tripod!) But, on the topic of a portrait: what kind of results are you after? With a DOF of 3 cm you are able to get your subjects nose in focus. DOF won't reach to their eyes or ears.
But, ignoring specific depth of field for a moment and trying to better answer the question of continuous or single AF mode: yes, continuous mode can be very helpful in achieving focus lock when using shallow depth of field. Most specifically, look at sports photography: shooters are after slim DOF to highlight one or a few players and the players are often moving fast. Continuous AF is often a good way to follow them to get an in-focus shot (or, more correctly, continuous AF is an important part of following them to get an in-focus shot).
There's more than one way to create the shallow depth of field that is often associated with portraits, however. We most typically talk about using a large aperture to do it, but another thing to consider is subject-distance relationships: the farther away the background, the more out of focus it will be. Depending upon lens focal length and aperture, f5.6 or f8 can create the effect of a shallow DOF if the background is far enough away. Likely helpful reading: What exactly determines depth of field?
I would not rely on continuous AF for that purpose.
You have a choice about how much DOF you use. There is an unhealthy obsession these days with extremely small depth of field in the mistaken belief that extremely blurred backgrounds are always desirable. In fact you just need some background blurring to create a visual separation, but not extreme amounts. Good composition and lighting will do the rest.
Too much background blur is just as distracting as too little.
So if "tiny DOF" is causing you a problem with focus, the solution is simple : stop using it !