It would appear you are not alone with this problem.
I've just been doing some research on this for you.
I have only really one idea as to why this is happening but i'll get to that in a moment.
Firstly, check this page out. let's see if the problems suffered here are the same as yours.
www.carcomplaints.com...
I presume you've got an auto trans by the way you say it revs up.
One poster there said his problem was fixed by changing the alternator.
Some cars computers can go a little of key occasionally, disconnecting the battery for a day sometimes helps reset the computer.
I was originally thinking along the lines of the kick down control of the box, but I had another idea.
I got onto thinking about gears slipping and clutches (auto's have convertors)
and I was wondering if the viscosity of the gear box oil is wrong. You might really need a hicker oil to keep the torque convertor stable.
These people seem to notice the problem on a long run, when the oil is really hot and at its thinnest point. A thicker oil may actually stop the
slipping.
Changing the gear oil for a thicker one is a lot cheaper than buying another alternator or another gear box, and wil take less time than disconnecting
the battery for a day.
I can't think of much else seeing as this problem is being talked about a lot on the accord...
just check the chat for the
2003 model
I really hope this helps.
now at least i can go down the list ,i have already changed the alternator
once before so now ill try a thicker oil as you suggest and also see if its an electronic problem. thank you very much for the link i was not aware
of the honda problem. 
