What I meant wasn't that parties would moderate...that's hardly a given...but that the electorate would tend to slide back towards 50-50 (or at least being ideologically competitive) as a rule.
Thomas Jefferson's "Democratic Republicans" had essentially undisputed one-party rule for 28 years. When that finally ended, it wasn't due to the revival of the Federalists -- the Federalist Party was *dead*. It was due to the Democratic-Republicans splitting into two factions ("Jackson men" and "anti-Jackson men").
Of course, ideology and party can get disconnected...the Dems had control of Congress for most of 40 years, but factions within the party messed with the ideological situation therein.
This sort of thing can go on for a long, long time.
A lot of this also comes down to the fact that, at the national level and assuming no structural issues (generally malapportionment, though gerrymandering and problems with the main opposition can play a role as well),
We do, of course, have massive structural issues in the US. People who do comparative analysis of the structure of different democratic systems tend to say that the US bicameral/Presidential single-member-district gerrymandered-House malapportioned-Senate electoral-college system is really pretty messed up. The states are slightly better off since the Supreme Court restricted the degree of permitted malapportionment in the Baker v. Carr series of cases in the 1960s, but still have problematic bicameral gerrymandered systems; Ohio is gerrymandered so that 50% of the vote will get the Republican Party 75% of the seats. The NY State Senate is actually malapportioned to the maximum extent permissable by court precedent, with the "Republican" districts all having 5% fewer than the ideal number of residents and the "Democratic" districts all having 5% more. (The NY Assembly is malapportioned the other way.)
it's rare to see one "side" have more than a 15-20 year run in control in a democracy that is mature.
Sure, but (a) we do have serious structural defects, and (b) when the voters eventually do manage to throw the bastards out, it doesn't mean that the current opposition is going to benefit. At the moment I'm pretty sure it *won't* mean that; people are really mad at the incumbent-protection organizations masquerading as political parties, and are grasping at straws trying to find alternatives.
Either the existing parties will re-form and become something totally different (historically, the Republican Party and Democratic Party both completely changed ideologies during the 1960s-1980s, and the Democratic Party completely changed ideologies a couple of times before that). Or parties will fall and new parties will arise, as with the demise of the Federalists and the Whigs and the rise of the Republicans in the 1850s. Unfortunately, our structurally-deficient system makes it hard for this natural change to happen smoothly. (It happens much more smoothly in proportional-representation systems -- they have their problems, but in those systems, the parties shift to reflect the public mood in a matter of years, rather than decades.)