I saw this question asked in various places, but no satisfactory answer was given. While only Honda knows the answer with certainty, I think there is enough evidence between my own experience and reports on the web of failing Accord and Odyssey transmissions to support a theory.
In 2004, Honda issued a recall for the 2003 Accord. The transmission was to be checked for discoloration of certain metal parts (from overheating), and the transmission was to be replaced, or in the absence of enough visible (thermal) damage, an oil jet kit was to be installed.
The oil jet kit was supposed to provide extra cooling (enough to get most transmissions on the road through the extended warranty period).
So clearly it was known in 2004 that the 2003 Accord transmissions had a thermal problem due to faulty design. The transmissions were overheating and there was concern about failure.
When a transmission overheats during normal operation, its thermal design is faulty. The transmission fluid does not transport the heat away from the source fast enough. The system overheats, and the fluid itself and certain other parts can no longer do their job. The fluid loses viscosity and does not lubricate, metal parts warp, gaskets fail, valves get clogged, and the transmission can no longer function. The transmission fluid fails, and soon thereafter the transmission will fail as a result.
I believe that the symptoms (erratic shifting once the transmission warms up, very dark transmission fluid soon after it was changed) are a strong indicator that the theory of thermal problems is correct.
What I do not know is whether Honda addressed this issue in the design of the 2004 models and later, and if a replacement transmission is less likely to suffer the same fate. This remains to be seen. Hopefully, our replacement transmission will outlast the car regardless.
In reference to this post I received an email with a link to this page. It contains a much more detailed explanation than I could ever give. In essence, the claim is that Honda engineered a new type of transmission in the 90s – hydraulically actuated manual transmissions. They originate from F1 racing, are easier and presumably cheaper to make, but don’t shift as smoothly as conventional planetary gear ATs. To overcome this and to address customer complaints, Honda applied a variety of tricks to make the transmission engage more gradually, all of which contributed to the overheating. Read the article for details.