That image disappearing problem is called, in fact a "camera clipping" problem. It's not actually a problem but more an issue as if we hadn't got it we couldn't dive into walls or stuff like that.
The issue has to do with the position you are looking the model at and it's way more recurrent in parallel because in perspective you have a clear notion of where you are. Cycling from parallel to perspective modes might cause the issue if you get to close to model by zooming in a lot in perspective, and then you cycle to parallel and zoom out. As your camera is in fact very close to the model it clips the model either in perspective or parallel. However in parallel there is no distance to subject as there is no point (2 or 3 point) perspective. If you zoom out camera sticks to place but the parallel view get's smaller. In perspective camera moves away from the model.
That is why switching from parallel to perspective causes the issue but also corrects it if you know how to apply the right zooming.
Large models are specially prone to this kind of stuff happening.