As another reply stated, there are neo-pagan religion that attempt to continue to traditions of those civilisations. However these practitioners are not descendents of those who had practised the religions and instead are a kind of convert. It is hard to tell when a religion died since there likely were isolated practitioners who still followed the ethnic religion - an example is the Christianisation of Scandinavia. Christianity did have a strong foothold in Egypt befor the Islamic conquest and the continuing existence of the Copticonic religion can attest to this. The last Pagan emperor of Rome was Julian the Apostate. Emperors who followed him ordered the destruction of Pagan temples and the altar in the Senate was removed by Constantius II. This does not indicate a lack of pagans, however, and there would still have been practitioners after the persecutions.
I would have guessed it suffered its death nail under the Fatimid caliphate, which is why we ask for sources here. It slowly weakened due to synchretism, or the blending of religions, with each group that conquered it. First with Alexander the Great, then Rome.
Another aspect is the death of the hieroglyphic language, so a lot of the religion lost its meaning. Before Islam had a chance to snuff it out, Christianity handed Lower Egypt and most of Upper Egypt it's final bow.
http://historum.com/ancient-history/47360-when-did-ancient-egyptian-religion-die-3.html
http://www.bbc.co.uk/history/ancient/egyptians/egypt_end_01.shtml
There are people who believe in them. But these are recpnstructions not continuations of the religion. It's called neo-paganism, there are various branches of these religions ranging Asatru (Germanic) to Hellenism (Greek paganism) as well as countless others. http://en.wikipedia.org/wiki/Modern_paganism http://en.wikipedia.org/wiki/Hellenism_(religion)