2001 Honda Civic EX low gas tank/hesitatio

My 2001 Honda has only 33,500 miles on it but I think it's cursed by the lemon gods. Aside from having been t-boned on each side, and the whole outer structure having to be replaced (aside from hood, roof, and trunk), I've had this annoying problem that occurs when my tank has 1/3 or less gas in it. When the tank is full or above 1/3, it seems fine, runs great. But when it falls below 1/3, it starts to miss and hesitate when I accelerate. My check engine light went on when this first started happening, code PO171, system too lean, bank 1.

When this first started happening (over 2 years ago) I took it to one of the local dealers. I took it in 3 times. Each time they couldn't figure out what was wrong; once they replaced the oxygen sensor and the other times they just added something to the fuel (like a cleaner). The check engine light would go off for maybe a week and then it would go on again and the original problem was still there even after they replaced the oxygen sensor. They ultimately told me they didn't know what was wrong. Other people have suggested that it's the fuel filter or fuel pump but I don't want to replace parts that don't need replacing. It's expensive! And why does the problem only happen when my gas tank is getting low?

So it's time for me to go to DEQ and to renew my registration, but I can't pass DEQ unless the check engine light is off. I could probably have the dealer temporarily turn it off, but I'd rather figure out what the problem is and get it fixed. Has anyone ever heard of this problem? What do I do?

Help! And thanks!