This is a new glitch that seemed to appear after they recently fixed the problem with the codeshares on JL/CX not appearing at all as reported in other threads. I just booked a roundtrip RDU-SIN. The fares would show up AA.com, my corporate AMEX travel website, and ITA and not be bookable (multiple days). It turns out there was not availability in these fare buckets. Interestingly enough, EF did not show availability. I ended up booking RDU-JFK-HND-SIN-HND-JFK-RDU via the phone. The phone agent was able to book the "H" fare that was available and shown via EF. AA.com, ITA, etc continue to think there is an "L" fare available. I hope they fix this soon. It's a PITA to cross-reference AA.com/ITA with EF.

UPDATE: the issue with my itinerary was the RDU-JFK leg. The "L" fare is not available on the codeshare, only with the JL flight number. When booking the AA codeshare, "H" was the cheapest fare. EF showed this. AA.com/ITA/etc screw it up, so you must book via phone.