(This depends on the teacher or lineage.)
Generally if you stay too long on a object the following can happen:
- get attached to it or obsessed with the object. Say you have a pain in your stomach then you will think this might be food poisoning. Also why is it lasting so long? It is supposed to be impermanent but why is it lingering. Likewise all kind of thoughts will keep arising due to the object.
- you can miss out on other experiences in other areas. Main thing is that you should be able to see all experiences through out the body. Staying in one object means that you miss many more subtle experiences. Say your stomach hurts but there is a itching on the head. If you stay with the pain you miss the itching.
So best is to systematically change the objects (emphasis on systematic and methodically here so you don't miss watching experiences even on a small part of your body, i.e., you have to make every inch of your body sensitive to sense the subtlest of contact / sensation, e.g. the air touching your skin in absence of any other sensations. To see things as they are you have to horn your recognising or conscious part of your mind / aggregates to register the subtlest of realities) so you experience everything on your body at most waiting on one object for for only a few minutes or so. If you are aware of the breathing, then you can see effects on it. In my case I stay on the breath only for few breaths. (No counting the breaths.)
Likewise if there are any parts of your body which is not sensitive enough to register any input / sensation (there is an object as your facilities are in contact with something or the other by your consciousness is not strong enough to recognize it), you have to wait on that place for a short time to see if you sense something.
You have to be equanimous in facing the sensations. In the absence of craving and clinging, your perception / mental reaction towards such experiences will become weaker and weaker. Also your stop putting fuel to the fire by creating new fabrications which will create further sensual experiences in the future.
As you do this you will start seeing things dissappear faster and faster until it disappears instantly once your attention comes to the object.
Any object, arises and passes away with such rapid succession. When you are sensitive to recognise it when your attention is brought to the object itself then you will see it happening. Otherwise by staying with the object your mind can get a bit concerned and then you will start seeing the arising and passing. (Keeping in mind the above arguments. ) In the latter case if the object is something like pain sometimes it may pass away before you can get concentrated enough to see the phenomena arising and passing. (At a grosser level this is arising and passing away also. ) Any case don't get excited or disappointed.