Comedy Central’s parent company, Viacom, had a contract going with Hulu which had a wide number of series under its umbrella, obviously including The Daily Show, and once that contract expired recently, new episodes of the nightly chat show stopped showing up in Hulu’s daily lineups, and all past episodes will soon be removed.
Many other Comedy Central hits like Chappelle’s Show and @midnight are already gone, so it isn’t just the Daily Show fans in Hulu’s subscriber base that need to start heading to Comedy Central’s website to stream new episodes.
That may sound like a sarcastic and super-obvious answer, but it’s basically the only answer at this point, as The Daily Show may take a while to find a new home on any standalone streaming services.