My somewhat shaky grasp of Tamrielic History (from in-game books I maybe 1/2 remember) is that you have the "Mythic Era", during which the Ayleids, who were Daedra worshippers, ruled Tamriel at the behest of the Daedra Princes, and in particular, Mehrunes Dagon. Men, Argonians, and Kahjiit were slaves of the Ayleids, and were often killed/sacrificed to Mehrunes and the other Daedra. St. Allesia then appealed to Akatosh to help men to be safe from the Daedra, so Akatosh forged the Amulet of Kings, which is used to light the Dragonfires, which create a barrier sealing off Oblivion.
My understanding then, is that Allesia's descendant, Reman Cyrodiil founded the first Cyrodiilic empire. This ended, and their was an interregnum, known as the 2nd Era, during which there was no empire(?), then Tiber Septim (who, presumably, is another descendant of Allesia) recovered the Amulet of Kings and founded the 2nd Cyrodiilic Empire, and the Third Era encompasses the reign of that dynasty.
So, the question is, why didn't the Oblivion Gates open during the 2nd Era interregnum? Is it because there was no 'agent' in Mundus to accomplish necessary rituals (e.g. in TES IV, we have Mankor Camoran and the Mythic Dawn acting as agenst of Mehrunes Dagon and the Daedra)? Did the Daedra actually need agents in Mundus to open the gates, or would the failing of the Dragonfires be sufficient to allow Dagon to once again enter Mundus?
Are there other lines of Allesia's descendants that aren't of the Septim line? In Oblivion, much of the Lore revovles around the mythos that a Septim must use the Amulet to light the Dragonfires, but sometimes religion, lore and history are . . . manipulated to serve those in power (e.g. the divine claims of the Egyptian Pharaohs, or the claims of divinity of Roman Emperor's, and more recently, Japanese Emperors). Now, of course, in the world of the Elder Scrolls, there is at least some truth to the claim, in that the Dragonfires did prevent Dagon and has armies from entering Mundus. But the question is, couldn't *any* descendant of St. Allesia/Reman Cyrodiil have used the Amulet of Kings?
We know that Martin Septim was an illegitimate descendant, and so could use the Amulet of Kings. I remember one or more of the books in Morrowind and Oblivion talking about one of the Septim dynasty who was notorious for his promiscuity. How is it possible that, by the time of Uriel VII, 1/2 the Empire aren't descendants of Tiber Septim? I would imagine that, given the history of feudalism in Europe, every count, baron, and minor noble in the Empire would be descended, at least distantly, from the Septims. Of course, the story of TES IV still basically holds true, because even if there were many descendants, the last thing you want is a war of succession at a time the land is already threatened by outside aggressors (in this case, the Daedra).
[Edited to fix spelling mistakes]