The I fare for this route requires a minimum of a 7 day stay. The OP's r/t is less than that so AA.com would not sell it to him.

EF is correct in showing the availability of I inventory on the MIA-LIM-MA segments. If you then click on the link at the top of the Flight Availablity results page that says "View Fares for DCA to LIM on AA", you will go to the Fare Results page (if you are a Premium EF subscriber). If you do, you will NOT see the I fare listed. Why? Because it is not a valid fare for the r/t dates requested.

Now, go to the top of the fare results page and click the link "Refine Search". Uncheck "Validate Fares". Click Search. Now you will see the I fare. Look under the Min/Max Stay column and you see 7/30. The fare rules also has the details.