^Exactly. It's made more clear in the codex that the relays are just that; paired 1:1 relays. The Citadel is by design the only device that can control them all.
As for the previous cycles, the truth is, we don't know exactly what complications the Reapers may or may not have encountered. All we have to go on is Vigil's account of how the Protheans were caught unawares and the assumption that all previous cycles ended more or less the same way. But that's all it is, an assumption. Despite Vendetta's assertion that the cycles followed the same patterns of revolution and dissolution, those patterns could have been expressed in almost countless fashions.
Just comparing the "Citadel Council" civilization with what little we know of the Prothean Empire it's apparent that not everything goes "exactly" as the pattern dictates.
I was actually watching Sagan's classic Cosmos series the other day and the episode in which he talks about the Heike Crabs
and it occurred to me that a similar process of unintentional artificial selection could have taken place with the Catalyst and galactic civilization. Eventually, totally without intending to do, the Reaper harvests produced civilizations adapted to overcome the harvests. This is as good an analogy as any I can think of to account for how the crucible could have passed almost blindly from one civilization to the next. There way also be shades of chaos theory in there too, but it'd take someone much more well versed than I to expound on the subject.
There's also the fact that ideas are notoriously difficult to destroy. Admittedly in the real world we've never been able to test this principle on such a scale and across gulfs of extinction, but the principle is basically sound. The closest we've come is the dark ages, where despite centuries of neglect, obscurity and the best efforts of book burners and witch hunters, valid scientific knowledge from antiquity has managed to survive into the present day. Likewise there's a plethora of very well known and astonishingly wide spread cultural stories who's true origins are so old that it's damn near impossible to even know from whence they came, much less whether they have any basis in fact.