We have a 2006 Honda Civic & had 2 main computers replaced last summer. The “check Fuel Cap” message was flashing for close to 3 weeks despite checking & tightening the cap during 3 fuel refills. Despite the car being under warranty, the dealer charged $69 to reset the computer as they felt the cap must have been loose. Honda central (which is now on speed dial after last summer) was little help. Does this year / model have computer issues or are we just unlucky? Know anyone who wants to buy a '06 Honda with 34,000 miles?
These cars are in general very trouble free, so find a dealer who wants to actually fix the problem. It’s clear that there’s a malfunction with a sensor or there’s an issue with the fuel system that needs investigating. You paid them once, but don’t pay them again.
Be careful where you go for warranty work. Dealers take car of customers in this order: paying customers first, in-house sales warranties next, and outside sales warranties last. You are at the bottom of the list if you go somewhere else. I suggest that you find out how long it will take until they can get to it on the phone before you make any commitments.
You could just buy a new cap and give it a try. That may be the only problem and avoiding the hassle would be worth the cost of the cap for me. Not only that, but it is an easy do it yourself repair.