Are you the original owner? If so there is the question of how it was broken in. Also the type of oil has a relationship here (fossil or synthetic). If you have always used fossil-stay with it. If you recently switched-go back.
The amount of oil you are using is ABNORMAL, period. Less than a quart in 3000 miles is fairly typical for many of the owners. I use nearly none and have over 31k on the odometer, and that includes track time at Pocono.

Pester the dealer and Honda support-call the 800 number-they will work with you to resolve the problem.