2003 Accord Transmission light

I should start by stating clearly that my 2003 Accord has had no
problems driving, shifting, or with gas mileage.

A few weeks ago, while driving on the highway, the light on the dash
that indicates what gear the car is in started to blink. It continued
to blink for the rest of the drive. Every time I've used the car
since, it starts up with the light not blinking, and after being on the
highway for 2-3 minutes, it starts to blink and continues until I turn
the car off. We looked in the manual, but there was no info about the
light.

We took the car in for an oil change and asked the dealer about the
light. The service advisor said he didn't know, but that they'd run
the diagnostics and see what they could find out. The diagnostics
indicated that the car had some kind of problem with the transmission.
The dealer says that the car isn't going into overdrive on the highway,
and that's what the light blinking means. Their advice was to buy a
new transmission. That seemed like overkill, so instead they changed
the transmission fluid. The fluid has now had several days to work its
way through the transmission, but the light is still blinking after the
car has been on the highway for 2-3 minutes.

I understand that transmissions eventually wear out, and I've bought
new transmissions for other cars, but this one has 84K miles on it, and
is driving without any problems. I understand that I'm losing some
fuel efficiency by not using overdrive, but given how few miles I put
on my car, I can't really see how it is worth it for me to buy a new
transmission to solve that problem. The dealer also seems to be a
little vague about exactly what is wrong, and so while I feel pretty
confident that a new transmission would make the light stop blinking,
it seems like an awfully big thing to replace in this situation.

Any advice?

Thanks!

 

Is it a 6 cylinder? Call up Honda and tell them about the problem. They
may authorize a fix for free.