The ability to selectively focus on a subject and isolate it is a result of depth of field. Depth of field is the range of distances from the camera in which an object will appear to be in sharp focus.
The depth of field is determined by a combination of the physical size of the projected image on the imaging medium and the size of the aperture in the lens. Small images, whether by the use of wide angle lenses, small imaging mediums, or a combination of the two, give great depth of field. Small apertures also give great depth of field. Because you cannot change the lens or sensor, the portrait mode will attempt to use the largest aperture possible.
This means that point and shoot cameras, with their very small image sensors compared to digital SLRs or 35mm film, have a small projected image and a large amount of depth of field. Even if the aperture is wide open, there can still be too much depth of field to isolate the subject. If you zoom in to the camera’s maximum focal length, you may be able to decrease the depth of field enough to isolate the subject. Dimming the lights may also help, since the camera may not have a shutter speed fast enough to properly expose the image at the camera’s maximum aperture if the scene is very bright.
If you still cannot, using manual focus will allow you to focus on a point in front of the subject so that the far limit of the depth of field extends just past the subject. This is difficult to do with a point and shoot, though, and many point and shoots do not even have manual focus capability.