It used to be the go-to show for forensic news satire. But thanks to Twitter and co, it’s up against far faster – and often just as sharp – competition. Is it time for the final edition?

To paraphrase Jimmy Nail: if you love something, set it free. I'm starting to suspect this might be the case with Have I Got News For You. The show used to be fresh and vital, razor sharp and gleeful in its dismantling of the news. But it's a shadow of its former self now. It lumbers along, as best it can, taking easily telegraphed potshots at targets that are already dead. It wrings out titters where there should be guffaws. It used to be Lenny Bruce, now it's Bruce Forsyth. I say this with a heavy heart, but I think it might be time for a dignified retirement.

It's not hard to see where the show went wrong. The internet killed Have I Got News For You, plain and simple. Back in the show's heyday, you could rely on it to deliver the definitive satirical reaction to the news. But now it's competing with The Daily Show, humour sites such as The Poke and millions of would-be wags on Twitter who fall over themselves to mine every last microLOL from every single news story a nanosecond after it breaks in a rabid bid for retweets. By the time Friday night rolls around, all Have I Got News For You has left to work with is the chaff.

Worse yet, the show doesn't feel like a unit any more. At its best, the show is a well-oiled machine – two team captains, one silly and one sensible, working with a like-minded host to bring either the best or worst out of their guests. When Have I Got News For You is firing on all cylinders, the interplay between Ian Hislop and Paul Merton is hard to beat.

But such moments are now rare. Merton used to liven up the show with dazzling flights of fancy, but he now spends about three quarters of every episode looking impossibly bored on the right of the screen, raising his head only to say the word "sparrow" or to do another exaggerated double take. And this effectively means that the show is Hislop's now. And while his political point-scoring shtick is fine – brilliant, even – in small doses, 30 minutes of it each week can get a bit wearying.

Perhaps that's unfair. Have I Got News For You isn't just half an hour of Hislop. It's 22 minutes of Ian Hislop, plus four YouTube videos that you've already seen 10 times and an uncomfortable bit where everyone acknowledges a story too serious to be joked about and the audience responds with an awkward mixture of clapping, groaning and silence.

In fact, this last point is my biggest problem with Have I Got News For You. Ever since the Jimmy Savile scandal came to light, and the BBC bodged its response, Have I Got News For You has become uncomfortably moral. With Savile, it had to acknowledge the story, react to the BBC's fumbling and – in Merton's case – deny the existence of a supposed incident on the show in 1999 where, according to a transcript circulating on the internet, he accused Savile of paedophilia. None of which was very funny, and being funny is the point of the show.

Since then, these uncomfortable moments have happened time and time again. Last week, it came during a discussion of Nigella Lawson, although the whole episode seemed to have a general air of discomfort. Maybe Have I Got News For You was just having an off week. But what an off week it was. The team captains looked bored, the guests contributed nothing; and in Robert Lindsay, it found perhaps its worst-ever host. Vast tracts of the episode seemed to go by without anyone so much as smiling, let alone laughing.

This week has to be a step up. The host will be Kathy Burke, who always brings a dynamic to proceedings. And the inclusion of Miles Jupp as a panellist is never a bad thing, especially since Hislop is never anything less than fully delighted by his presence. But the fact remains that Have I Got News For You is a show on the slide. Could it be time to quietly put it out to pasture?