Actually he can do infinite things at infinite times, as he exists both inside of time and outside of time. He's literally everywhere and everywhen all at once. Such is the nature of any God, especially the God of Time. In Morrowind, Vivec explains what it is to be a God, and part of that is existing in multiple dimensions and times all at once. Tiber Septim for instance has been waging perpetual war against the Aldmeri high priests since before time began, and long after it ends.
As for the prophecy of the Elder Scrolls, the trailer makes it clear that certain portents herald the arrival of Alduin the Devourer. I'm not sure if they're always the same in every single Kalpa, but in this one events like the breaking of the Staff of Chaos, the activation of Numidium, the removal of the enchantments on Shor's Heart and the Oblivion crisis seem to herald his coming. Whether or not these are simply omens or if each one of them broke some kind of metaphysical chain holding Alduin back remains to be seen. I'm reminded of the "Seven Fights" series and Alduin making some remark to the Leaper Demon about how they always try to stop him. so it's entirely possible that in previous Kalpas, a Dragonborn has appeared and ultimately failed.
One common thread of all these games' storylines is that something is broken at the end every single time, whether it's a physical object or a metaphysical concept. Every time. When the Staff of Chaos broke, not only did a physical object, but the Imperial Simulacrum as well. In Daggerfall, the long stalemate/perpatual wars were ended by the Miracle of Peace. In Morrowind, the enchantments on the Heart of Lorkhan were broken, which also broke the divinity of the Tribunal and the House Dagoth high priests. In time this would lead to Morrowind being quite literally broken, when the last of Vivec's power faded. In the shorter term, it led to the break of the Temple's authority in Morrowind, and the sanity of Almalexia. Hell, even Bloodmoon deals with the breaking of a cycle - for the first time, Hircine is defeated at his own hunt. At the end of Oblivion, it seems the Covenant was broken when the Amulet of Kings shattered. Later, Umaril's connection to the spirit world was permanently shattered and he ceased to exist. Later still, the cycle of the Greymarch ended for good.
What's all this leading up to? All these broken cycles? Will the world itself finally break or will Alduin?
I'm reminded of the ancient story of Yahweh vs. Leviathon, which predated Judeo-Christian mythology by some many hundreds of years but still finds its way in a fashion in Psalm 74:
It was you who split open the sea by your power;
you broke the heads of the monster in the waters.
14 It was you who crushed the heads of Leviathan
and gave it as food to the creatures of the desert.
15 It was you who opened up springs and streams;
you dried up the ever-flowing rivers.
16 The day is yours, and yours also the night;
you established the sun and moon.
17 It was you who set all the boundaries of the earth;
you made both summer and winter.
Does the description of Yahweh here remind you of anyone? Who in the Tamrielic mythology is thought by men to have fought the dragon? To have opened up the springs and streams? To establish the boundaries of the earth?
Will the Dragonborn "crush the heads of Leviathan" and "dry up the ever-flowing rivers" (of time/rebirth)?
Maybe I'm seeing a connection that isn't there, but MK has stated before that many elements of TES literature are rooted in Judeo-Christian scripture. I believe there is a parallel here.