Regrettably, this ends up being a much more "AskLawyers" question than I expected. That's because of an interesting -- and historically grounded! -- quirk.

Namely: the Seventh Amendment doesn't apply to state trial courts. That's because the Bill of Rights wasn't originally applied to the states -- it was intended solely as a limit on federal power. While that changed with the Fourteenth Amendment, which applied most of the Bill of Rights to the states ("incorporated the Bill of Rights against the states," in legal jargon), the Seventh Amendment right to a jury trial in civil cases seems to have been... left behind, somewhat, with state constitutions filling the gap. That means that the $20 limit is basically moot for state court; it's why if you sue your buddy over a $15 or $25 bar tab in state court, you'll be laughed at and sent to Small Claims Court.

The $20 limit also doesn't come up much in federal court, because it's pretty hard to get into federal court in the first place. Federal courts can only hear "cases and controversies" (see the Constitution's Article III, Section 1), which is a far narrower term than it sounds, and in general, they can also only hear two kinds of cases:

1. Cases pursuant to their federal question jurisdiction: a case resting on a question of federal statutory or constitutional law, 28 USC 1331

2. Cases pursuant to their diversity jurisdiction: cases between citizens of different states, where the amount in dispute is over $75,000 28 USC 1332

That means a federal case premised on less than $20 is only ever going to get to federal court if it turns on a question of federal law -- like securities fraud -- and those tend to be big-ticket cases for millions of dollars.

Additionally, once you're in federal court, there are a number of procedural quirks and devices that make it less likely you'll ever get to assert or litigate your right to a jury trial. Juries are triers of fact ("Did that guy commit securities fraud?"), not law ("Is securities fraud illegal?"). Over the years, the Supreme Court has taken a flexible reading of the Seventh Amendment (see Parklane Hosery below), giving judges more leeway to dispose of cases "on the law." In 2015 there were less than 5,000 federal trials nationwide, with only 1,800 of them being a true trial by jury.

So what's this mean for your question? It means, basically, that the $20 limit doesn't come up that often! So infrequently that I haven't been able to find a single case where the constitutional, $20 threshold determined the outcome of the case. Other limits on the federal court system make jury trials so rare that the question just... doesn't come up.

Sources & Recommended Reading

• Akhil Amar's book, America's Constitution: A Biography

• Akhil Amar's law review article on how the Bill of Rights applies to the states, "The Bill of Rights and the Fourteenth Amendment," http://digitalcommons.law.yale.edu/cgi/viewcontent.cgi?article=2005&context=fss_papers

• Several cases on the Seventh Amendment's place in the constitutional order are helpfully summarized by this American Bar Association bulletin: http://apps.americanbar.org/litigation/committees/appellate/articles/fall2015-1215-ripe-incorporation-seventh-amendment-civil-jury-trial.html

• Scalia's excellent law review article summarizing standing, an important limit on federal court jurisdiction: "The Doctrine of Standing as an Essential Element of the Separation of Powers," http://suffolklawreview.org/wp-content/uploads/2015/11/Scalia_17SuffolkULRev881.pdf

• A good case on what the jury-trial right buys in federal court: Parklane Hosiery Co. v. Shore, 439 US 322 (1979), https://scholar.google.com/scholar_case?case=7479573211945418487&q=%22seventh+amendment%22+%22twenty+dollars%22+applies+to+states&hl=en&as_sdt=3,33#[25]

I've always wondered this. For anyone answering this, has the been any serious attempts to amend or strike that clause?