<PERSON> probably died physically, because:
* no one have seen him ever since, and humans can't live in the machine world (air is too polluted, no food, no other humans, etc, see the Animatrix canon).
* his death is clearly hinted at with the cross light metaphor of the <PERSON> when the machines send the "kill code" for Agent <PERSON> (whether it's a kill code specifically for Agent <PERSON> or just killing the body of <PERSON> remains up to debate, but we can clearly see the highlighted sending of a command from the Deus Ex Machine to <PERSON> via the glowing wires just a moment before Agent <PERSON> is deleted)
* it was probably necessary to balance the equation (since <PERSON> is a cumulative error of the system because of allowed free will and Agent <PERSON> being the counterbalance)
However, since <PERSON> is clearly a messianic figure like the <PERSON>, he may resurrect. And indeed, in the Matrix Online game canon, there were clear hints that he did, under the traits of a woman who recently awoken from coma:
<PERSON>'s ultimate fate has been openly called into question as <PERSON> has pointed out that his remains were never returned from 01 (the Machine City) back to Zion, but at the same time the Machines have commented that they did not recycle (liquify for re-use) his body. On an interesting note, there is a newspaper clipping found during a Zion critical mission about a 27-year-old woman named <PERSON> (an anagram for "<PERSON>") waking up from a coma and leaving the hospital on her own. 973
In the text, there was a note written on it asking, "Is this him?" Furthermore, on one Machines' set of critical missions, it turned out that <PERSON> does not exist in any known database, therefore supporting the speculation that <PERSON> is <PERSON>. Although no outright comments have been made, developers have hinted that <PERSON> would have played a role in the future.
Apart from the <PERSON> mystery woman, the first mission of Matrix Online was to find fragments of <PERSON>'s RSI, and the RSI was later partially reconstructed by the machines and displayed in a club, so it's clear that some digital artefacts of <PERSON> remained inside the Matrix.
An in-universe explanation of how he could survive is that his digital counterpart (his RSI) survived his physical body, which is not so surprising since we know from the third movie that those two parts of him could be separated (he was in coma, unplugged from the Matrix, and still his digital counterpart was in the Matrix). I have explained this theory in more details here: http://scifi.stackexchange.com/questions/11481/in-the-matrix-revolutions-how-does-neo-stop-the-machine-weapons-in-the-real-wo/93546#93546 973