It follows a pattern which changes back and forth over time. If it did not follow a pattern that changed predictably over time, it wouldn't be cyclical. Words have meanings and all that.
But there is nothing predictable about it. You have observed that a condition that is true more often then not was true in two occasions in the past. That has no statistical significance.
Alright, let's go with a concrete theory, a hard and fast rule. Using my previous definition of dominant party, and starting with the dissolution of the Federalist party: congress never changes unless it is either bouncing back to the dominant party, or the dominant party controls both houses and the presidency.
In all of US history I count 5 breaks from the pattern. 2 of these breaks occur when it cannot be identified who controls part of congress (tie in one case, it switched mid-way in another), in both of those cases a single senator flipping would cause the rule to hold true. If you don't count those, that's 3 elections that don't follow the rule, 92 that do.
Also where are you getting twice? First the democrats become dominant in 1825, then the Republicans in 1861, then the Democrats in 1933, then the Republicans in 1995. Did you actually read my post besides finding a single sentence to chop out of it?
Edit: The rule also holds fast if you view the democrat-republicans as part of the democrats first run of dominance and start the counting at the 7th congress/1801. This also extends the democrats original run of dominance to an even 60 years.