I have about 250,000 miles on my 04 TSX which has similar K series engine as in RSX and it started burn oil about 1 year ago. I have to add 1Quart every 1000 miles and i am tired of it. It does not matter what kind of oil, synthetic or convention, still burn oil bad. It has no blue smoke when I start the car in the morning so oil burn is not from leaky valves seals. Then I tried to use sea foam and it fixed the problem. Now it burns no oil with mobile 1 after 2000 miles. I made a video of it and hope it help those who has the same problem.

 

Marvel Mystery oil would've possibly fix this as well. I had this happen on a b20 swap of mine.