I'm sure DL would just say that the website is great, its been winning awards and the mobile apps and technology has been praised by the media. I'm sure they would deny there is a problem and until they start losing money or performing worse than AA, UA and to a lesser extent US, why would they have reason to believe that they are losing money?
I don't think DL is too bothered to losing consumers to Ultra Low Cost Carriers like Allegiant or Spirit otherwise they would actually try and compete on price with them.