How long would a Matrix iteration cycle last? I mean the time frame from a reboot to the next.
We don't know for sure, but the best estimate we get comes from Morpheus during his speech in Zion:
I remember that for one hundred years we have fought these machines. I remember that for one hundred years they have sent their armies to destroy us. And after a century of war, I remember that which matters most. We are still here!
Morpheus, The Matrix Reloaded
The Machines demonstrate that they are able to learn from the humans (e.g. Rama Kandra indicates that the Machines are learning how to love), so it is possible that each iteration of the Matrix lasts a little longer than the previous one. There is probably an upper bound on the length of time each iteration can last, though:
- the Machines can't get much better at getting humans to accept the program (they are already at 99%)
- the Machines need to periodically destroy Zion in order to check its power against them (and this coincides with the reboot of the Matrix)
- the Machines probably need to reset the internal time of the Matrix (i.e. set the clock back to approximately 1999).
- the Zionists evidently think the Oracle is a human since they trust her, yet Morpheus says that she has been with the Resistance "since the beginning". This means that the Resistance could not have been fighting the machines for longer than a human's lifespan as the Zionists would start to wonder how the Oracle is still alive after so many years and suspect that she's actually a program.
Note that the Matrix betas (the Paradise Matrix and Nightmare Matrix) probably lasted much less time since the Machines had not yet achieved 99% acceptance. Rejection of the Matrix grew much faster in the Matrix betas, so the betas had to be redesigned more often.
Although Morpheus' speech mentions 100 years, that isn't really possible and much more time must have passed than even Zion realizes. Why?
7 males and 16 females could not repopulate Zion to the many thousands within 100 years without memory, multiply that by how many times did the architect say the matrix has been reloaded under the current The One paradigm?
It must be several hundred years at a minimum for each reboot.