People seek out and consume news content more than ever before and newspaper website traffic is still increasing, but it still doesn't matter.
The website cannot "save" the newspaper model. Reporting quality, reliable news content and publishing a daily newspaper is not cheap and the ad revenue from a website is not nearly enough to sustain the business model.
When newspapers first started selling malayalam news their online product they would visit me with both a print and an online sales rep. Usually, the print rep was a newspaper veteran with very little knowledge of online and the online reps were young web guys with little to no newspaper or sales experience. Very few offered bundled ad packages with print and online, which would seem most logical and they often took turns talking, rarely discussing the other medium.