It's a long-standing tradition in TV that the topical and news shows take the holidays off. There's no edition of Newsnight today and there was no Question Time or This Week last night. Edgy comedy is generally dropped as well, in favour of heartwarmers. But, there at 10pm tonight is Have I Got News For You, not only surviving but, courtesy of the yuletide calendar, returning to the Friday night slot it held until the recent Thursday re-scheduling. Even though its official Christmas edition was last week, commissioners have contrived another.

One explanation for this break with broadcasting tradition might be that HIGNFY, which began in 1990, is strictly classified as entertainment rather than current affairs but the strongest reason for its continuation through the season of novelty and one-offs is its absolute reliability as a provider of ratings and quality comedy.

A telling way in which the success of HIGNFY can be measured is that it is itself a promising quiz answer. For example, which is the only TV show to have been a hit for a decade on BBC2 and then another decade on BBC1?

And dedicated viewers offered the answers "Alexander Armstrong", "tub of lard", "Ian Hislop" would have little trouble in providing the questions. Who has been the most regular guest host since Angus Deayton was sacked in 2002? Which cooking ingredient replaced Roy Hattersley when he failed to appear? Who is the only person to have appeared in all 352 episodes to date? (This is slightly a trick question: one permanent captain is far ahead because Merton dropped out of a whole series, feeling "stale".)

By the end of the Christmas Eve edition, Hislop will have done 353 and Armstrong will be even more dominant in the list of favoured stand-ins. But there is nothing inevitable about this success. The show has overcome events that have terminated other franchises: a move between networks, the loss of a regular presenter, periods of moral and legal panic at the BBC over broadcasting strong content.

Counterintuitively, though, the programme has benefited from editorial crackdowns following the Gilligan/Kelly affair and the Ross/Brand scandal. At times when news shows were heavily corseted, HIGNFY has been a licensed jester, apparently given greater leeway by the corporation's duty lawyers and gag police. For example, after the BBC was reported to have written to Eammon Holmes to reassure him that John Culshaw's The Impressions Show would cease to make jokes about his weight, Paul Merton turned almost every question into a gibe at the presenter's size.

This freedom is achieved partly because the programme can accommodate a range of tones. During the Kelly affair and the MPs' expenses scandal, Hislop would often depart from the comic remit completely and recite cold fact, in the manner of a parliamentarian reading details into the public record. The contrast between this journalistic approach and Merton's surreal riffs is one of the central strengths of the series and it also helps that the broadly rightish Hislop and the broadly leftish Merton provide an in-built political balance that has provided insulation against editorial busybodies at the BBC and in the national press.

Admittedly, the professional understanding between the team captains also triggered the franchise's biggest crisis which, at the time, was seen as potentially terminal. Although Deayton was fired by BBC managers, following newspaper allegations of sexual and narcotic indiscretions, his position had become untenable because the show's other two regulars sabotaged on air his attempts to manage the scandal, Merton famously appearing in a T-shirt printed with a ruinous headline.

This messy execution has been attributed by supporters of Deayton to his on-screen colleagues' alleged resentment about the fees he received for what they regarded as an easier role: the host has a team of gag-writers. But all the regulars on HIGNFY were handsomely recompensed and it has always been my view that the captains undermined Deayton because of aspects of their own characters. Hislop is a moralist, who believes that private behaviour can be relevant to public employment, while Merton has a deep concern, shown in his fascination with silent film, for the mechanics and structures of comedy: for him, the format of the show depended on the chair being a scourge of scandal rather than a source of it.

But, whatever the cause of those events, the dynamic between the host and the team captains remains central to the show's success, although it is still occasionally a source of weakness. There is a strong suspicion that Hislop and Merton, perhaps subconsciously, withhold or confer approval on the producers' choice. So Armstrong and Jo Brand, for example, are accorded respect; Bruce Forsyth was almost boyishly worshipped by Merton and the regulars rose to the comic potential of Boris Johnson's chaotic presentations, with his ignorance of celebrities and apparent unfamiliarity with the lines on his teleprompter. In other weeks, there is a sense that the energy level of the perennials reflects their judgment on the guest presenter. There seemed to be some needle, for example, between them and Jeremy Clarkson.

There's no doubt, though, that the concept of a shifting anchor has succeeded, against the initial instinct of most broadcasting critics and executives. For at least the first two years of impermanent presentation, there was a running assumption that someone would eventually get a long-term contract, with Armstrong and Desmond Lynam the favourites at different times. But the possibilities of allocating the number three dressing room key a week at a time soon became clear. Indeed, in a terrible blow to the position of the Presenter's Union in contract negotiations, the practice has now spread to Never Mind the Buzzcocks.

The uncertainty about who will be asking the questions has also helped the show's longevity. Any long-running broadcasting format depends on a careful negotiation between regular and original elements: the programme needs to look like the same show without ever falling into the category of same old show. Having 60% variability each week has kept the series fresh.

Appearing in one of the three open seats has also become a helpful entry on a CV. The extraordinary career autumn of Forsyth, including Strictly Come Dancing, was greatly helped by the benediction of HIGNFY, while Johnson's celebrity from his stints at the desk may well have helped, with at least some voters in the London mayoral election, to overcome some toxic political and private publicity in his past.

Such a fixture has the show become that it affects the way you watch other television. During The Apprentice, I fantasised about Lord Sugar as host (surely a booking to dream for) and Stuart Baggs as a guest.Every new channel controller – and Danny Cohen has just arrived at BBC1 – inevitably thinks: have I got new shows for you? But HIGNFY, at the moment, feels immovable.

Hosts to remember

The best

Bruce Forsyth In a career-relaunching performance, instinctively understood that he must take risks, including a Play Your Iraqi Cards Right round.

Boris Johnson BoJo's complete unfamiliarity with the script made him the only senior politician to be nominated for a Bafta best light entertainment performance award.

Jo Brand Earlier career as high-security mental health nurse guarantees iron control and redresses the usual strongly masculine tone of the show.

Alexander Armstrong Some actors have struggled as hosts. Armstrong, though, combines impeccable gag delivery with a pleasant presence.

The worst

Ann Widdecombe Famously a prude, she seemed appalled and the script had clearly been blue-pencilled to suit her. She threatened to walk out once.

Jeremy Clarkson The worst mistake is to try to show viewers the standup comedian you should really have been (Piers Morgan's error as a guest).

Greg Dyke Immediately revealed why his career had been spent running TV rather than presenting it.

Sir Trevor McDonald Apparently a comic manque – even launched News Knight, a HIGNFY rip-off on ITV – but his staccato news-reading style flattened the punchlines.