I just noticed something the last 2 times filling up. When I press the fuel door button, the dash changes to display a message "Please wait a moment" along with a fuel icon. A progress bar goes across the screen and then the fuel door pops open.
The car must be doing something to prepare for the fuel door to open? That would explain the delay in opening which I had previously perceived as the button not working on the first press. So it might not be a sticky door or button, but a different than normal design where they have a built in delay for some reason.