When you try to mentally visualize an image, for example a face, can you keep it constant indefinitely?

Not indefinitely, but the limiting factor is my attention quality and span. If I get distracted, the image disappears; if I try to pay attention to other things while continuing to visualize something, the visualization can subtly morph in response to the other things I'm thinking about, and it's hard to tell if it's morphing or not. (This effect seems closely related to priming.)

If yes, would you describe yourself as a visual thinker? Are you good at drawing? Good at remembering faces?

I'm a very visual thinker. I'm not good at drawing, but that appears to be a function of poor fine motor control and lack of practice; I have been known to surprise myself and others with how well I draw for someone who almost never does so. I'm not very good at remembering faces, either, but again other factors affect that; I tend to avoid looking at faces in the first place, since I find eye contact overwhelming. I seem to be very good at remembering other complex visual things, though.

I can hold an image/face steady for about a full second just sitting here. I could probably do better while meditating; so I think it's more an issue of 'can you concentrate' than anything else.

(I'm a pretty visual thinker, but my hearing-impairment also means I'm anomalous.)