the matrix - Why didn't the agents take over Neo's body?

Apparently, when someone sees something strange or unusual in the Matrix, it triggers some kind of red flag that tells the agents "come here and take over that body". We see it a few times during the movie, like in the subway station, with an old hobo, for example.

Couldn't the agents add Morpheus's and/or Trinity's faces to the list of triggering elements? If not, what about a self-repairing mirror?

My point is: why didn't the agents simply take over Neo's body? They had many opportunities before he was out of the Matrix. Can't they see through his eyes?

Plus, on a purely cinematic level, imagine how dramatic the scene would have been. Morpheus would have had a dilemma: getting rid of the agent would mean killing the potential One.

Answer

This makes sense if you consider the following to be the case:

1. Neo was probably not granted immunity by the machine upper hierarchy. I believe they only discovered he was the One when he was examined by the Oracle. At this point he was already unplugged.



2. Agents were after Morpheus, not Neo. They did not know Neo was important. He was bait.


3. Let's assume that, once a person's RSI is overwritten by an agent, that person becomes the agent till death. This assumption is supported by most scenes in the movies. It also explains why the agents did not take over Neo right up until Morpheus introduced himself. Neo is no use as an agent.


4. The rebels knew the possibility of Neo being taken over. There was a gun trained on him all the way to the hideout. At the first sign of transformation (which takes about 3 seconds) he would have been shot and the agents' operation would have been blown.


5. The only window of opportunity was from the moment Neo walked into Morpheus' room and to the moment he swallowed the pill (which disrupted his signal). This is the part that requires explanation.

So there are two possible answers:

1. The room with the red chair (or the red chair itself) is shielded. We've seen the same chair used during important conversations in the sequels (even the Keymaker sat on it when he laid out the plan to get to the Room).


2. The agents were relying on the bug to catch Morpheus because their alert program only kicks in when a person plugged into the Matrix notices an anomaly (such as a person disappearing into a phone receiver). Morpheus and the others did not use their 'powers' during their encounters with Neo. By the time the agents realized what had happened, the rebels were gone.