I have verbal assurance from American that they will be refunding me my $1200. And it only took three hours on the telephone to four different airline reps at two different airlines. Here's what happened:
Tickets have a ticket number (14 digits) and a record number (6 letters). You generally use the record number to do automatic check in, though you can use the ticket number as well.
My flights were/are El Al Tel Aviv to Newark to Cincinnati, American Cincinnati to Dallas to Toronto, and El Al Toronto to Tel Aviv.
It is also worth noting that my ticket is under the name "YehudaJonathan", since my Israeli passport is Yehuda and my American is Jonathan. Generally this causes no problem.
Bought and Reissued
I bought my ticket in June, and my travel agent reissued the ticket in July, with a different ticket number and the same record number, though the old record number was not printed on the new ticket: instead there was a "reference number", also six characters long but containing both numbers and digits.
I only discovered this the night before I left; I tried to check in online with El Al using my old ticket number but the old ticket number was not recognized. I quickly got the new one from my agent and successfully checked in for my flight. I had both the old and the new tickets printed out in my bag.
No problems getting through to Cincinnati on El Al/Delta. And no problems getting from Cincinnati to Dallas using the original record number.
The Problem Starts
When I tried to check in in Dallas, the record number didn't work. Rather, it worked but it was associated only with the old ticket number, not the new one. Therefore, the counter agents at AA could only tell that the old ticket had been changed to something but they had no idea what, or even with what airline. The Cincinnati to Dallas one did not suffer this problem because it was a separate leg of the trip, not associated with the El Al portions to and from Israel, and so remained under the original ticket number. Though why they let me check through two bags for free when traveling from Cincinnati to Dallas remains a mystery.
I gave them my new ticket as well, hoping this would resolve the problem. However, the AA ticket agents looked at the "reference number" on the new ticket, said that this isn't a valid "record number" for AA, and so this printout only applies to my El Al portion of the trip, not the AA portion. They never bothered to actually enter the new ticket number to check that. I didn't catch this; I thought they also checked both old and new ticket numbers, but I didn't insist on it. They also were not able, for a reason that remains mystery number two, to find my new ticket using my name and flight number.
The Resolution Starts
When I called AA today, they told me the ticket number they had associated with the record number and told me to find out what happened at El Al, since there was nothing they could do for me. Contacting El Al, they said that there was nothing wrong with the ticket, and was I sure that AA had used the correct ticket number. That's when it began to dawn on me that maybe they hadn't.
I called back AA, explained the story again from scratch to a sympathetic service rep, and we found the new ticket. Turns out that AA had assigned a completely different record number to the new ticket number, a record number that is entirely different from the original record number that El Al and my agent continue to associate with the new ticket. Mystery three.
Naturally, that ticket showed me as a "no-show", since I booked it but didn't use it. Of course, since I had bought a third ticket and used that, instead. She told me to go ahead and ask for a refund using their online refund system, explaining the story in the appropriate text field. It sounded like they were ready to refund the ticket and just had to fill out the form.
Unfortunately I hung up to do this, only to discover that the online form refuses to even let you ask for a refund if the ticket was issued as non-refundable and already used. Instead, the online form told me to call AA customer service if I needed further assistance.
Call rep four, who's overly sensitive and less sympathetic, and also, over the course of the next half hour ask me multiple times for the same information as her computer keeps crashing and she neglects to write the information down on any note paper, which is what she should have done the second time she asked me.
But after many minutes of holding and questions, she verbally assures me that they have gone ahead with the refund. She offers me no written, faxed, or emailed confirmation of this, but says I should be able to see this online once the refund enters the system. So I thank her and hang up.
It's now 9 hours later and I still don't see the refund in process online, but I'm hopeful.