Brakes...Funny problem
 

I have this funny problem with my Honda Accord 99 4Dr LX. (Automatic)
My car drives normally when taken out of the garage in the morning and its braking performance good. However, when I drive it for an extended duration without braking, (such as highway driving), the brake pedal becomes soft as rubber and I have to push it all the way down to the floor to make the brakes grip. However, the braking performance is normal. That is, the car stops within a reasonable distance once the brake grips.
This does not occur when I am in city driving, when I have to brake often and the brake feels as firm as ever and behaves normally.
I have checked the brake fluid level and it has remained well within the limits and I have not seen any oil drips on the garage floor ever.
Can any one help diagnose this situation?
Thanks!