I learned something new last night while speaking with an American Airlines booking agent. Lest I forget it, I'm documenting it here.
Apparently, when booking award travel, American allows domestic hub-city layovers of UNLIMITED duration when the stop is a part of a continuing itinerary to a foreign city. For example, if I want to fly to South America using my frequent flier miles, I can include a week-long stay in Miami on my way to Rio, or on the way back from Panama City. Next time I book a trip to Europe, I'm definitely spending some more time in New York City!
Some hub cities that are not domestic yet are within North America, such as Toronto or Vancouver, also qualify for this added flexibility. Also, because Hawaii is a domestic hub in route to the South Pacific, extended stays in Honolulu can be made on the way to or from places like Australia or New Zealand.
Alas, the same is not true with foreign cities. Just like exclusively domestic trips, stays are restricted to a maximum number of hours that makes leaving the airport impractical. Connecting domestic flights must be within four hours of arrival, while connections abroad must take place within 24 hours; the same time restriction applies for tickets that are purchased.
Even the 24-hour window rule is a great piece of information; if I have multiple connection options out of London or Paris, I can opt for the one that allows me to spend nearly a full day exploring the city!
UPDATE: The Frugal Travel Guy blog published an article about the most generous stopover rules
here.