D Inventory Available for 2 Segments But Not as Connection
 

I have routing LAX-JFK-MIA on 4/15/19 for DONE04. There is D availability on each of the 2 flights individually, but AA says it is booked as a connection and there is no D for JFK-MIA (even though EF shows D3). Is this something new? Any ideas how to get the segments to 'force'? For now I'm in Y JFK-MIA. (AA is correct. On EF I entered LAX-MIA with connection in JFK, and there is D0).

That is married segment logic. Long used by airlines to manage inventory and increase yields.

I have had this problem before and was able to re-book them individually. Just ask them to do a point to point.

... or have a > 24 hour layover in NYC.

Note that this may increase the +++ and introduce and additional cost in staying > 24 hours in New York.

As others have stated new AA has been doing more and more of this. I had it happen on a DONE earlier this year for SAN-PHX-LAX-JFK. I had to book PHX-LAX in L, but got the EXP upgrade 7 days out.

EDIT: What is your next stop after MIA? Maybe get a codeshare on that JFK-MIA leg.

Book As Point-To-Point
 

I have called 3 different agents on 3 different dates trying to get them to 'force' the point-to-point segments. Computer won't let them do it. I'm pretty sure one of the older RTW agents could make it happen, but they all seem to be gone since they combined departments.
My next flight from MIA is DFW-LHR.

Try HUCA. Good luck!

You may not be able to get any AA agent to book it the way you want, since they are increasingly monitored about not breaking rules, and the tools they are forced to use won't let them bypass such things. You can try asking them to book flights with six hours in JFK, since on a domestic set of flights, that should be sufficient to be a stop and not a connection. Or you could try adding an extra connection (e.g., JFK-DFW-MIA) and when you get to JFK, ask them to reroute you on a nonstop JFK-MIA.

With true married sector logic, it's not always this simple. When you hold LAX-JFK in D class, the system will close out inventory in D class (and often in all fare buckets) when you then bring up availability for JFK-MIA.

Depending on itinerary, could you use codeshares? Where are you travelling from prior to LAX and onwards from MIA? For example, if you were coming into LAX from SYD or HKG with QF/CX, those airlines *might* have a codeshare on LAX-JFK which could be valid even if you have a stop >24hrs in LAX. Or, if you are doing MIA-LHR with BA or MIA-SCL with LA, they'll possibly have their code on JFK-MIA. The married sector logic will typically fall apart when it involves other airlines as AA's system will read it as LAX-QF-JFK-AA-MIA.

Other partnerships like AF/KL have a more robust/sophisticated married sector logic which gives little difference if trying to mix AF/KL codeshares.

I understand married segment logic but not for the *ONE product. If all else fails try to book a stop at JFK , and then call back and change to your preferred MIA flight.

Codeshares might be an option, depending on if the OP has an overseas connection at either end of LAX-JFK-MIA, but I didn't suggest it in my post because the OP wrote "AA says...." which implies the OP is booking with AA. I've been told by AA agents that they are unable to see codeshares for AA metal and hence unable to book them. If the OP is using a TA, then the TA should be able to try codes.

I'm not sure what your point is; my understanding is that AA has set their systems to not even show codeshares on AA metal to their reservations agents.

Have you tried asking them to put you on the waitlist for "D" on the flights you want? Even if the inventory isn't available for immediate sale - a wait-list request might clear relatively quickly...