Critics often commend theatres for going off-piste and staging unfamiliar work by familiar writers. Playing with Fire, a little-known curiosity by Strindberg, is currently being performed to some acclaim at a small fringe theatre in London. Might that rule apply to David Mamet? Could it be that in decades to come – by which time Glengarry Glen Ross and American Buffalo will surely have the status of Strindberg's Miss Julie – artistic directors will re-examine forgotten oddities from the later phase of Mamet's career?

Perhaps not, given the alarmingly low stock of these dramas in the writer's lifetime. Race, a 2009 play in which a white defendant hires a black lawyer to defend a racially charged case, has just received mainly so-what reviews following its UK premiere. This comes less than six months after another Mamet play, The Anarchist, failed catastrophically on Broadway, its closure announced the day after opening. It managed only 17 official performances.

If anything, British audiences have been lucky. November (2007), an Oval Office comedy that achieved a respectable run on the back of a charismatic performance by Nathan Lane as a president dimmer than George W Bush, has never had a major production in the UK. And The Anarchist was originally planned to premiere in London, before being repackaged for New York, with Patti Lu Pone as a terrorist seeking parole and Debra Winger as her prison warden, engaging in dismayingly leaden exchanges about faith and redemption.

Race – though sometimes sketchy and preachy, as seems to be the manner of late Mamet – is, for me, by far the most satisfying of his theatre plays in the last two decades. Terrifyingly, the last absolutely first-class work was Oleanna (1992), his provocative dramatisation of an allegation of sexual harassment in academia. After Glengarry Glen Ross and American Buffalo, it completed the searing presentation of American values that made Mamet seem the heir to Arthur Miller and Tennessee Williams.

After that, we got The Cryptogram (1994), a slight piece about childhood; Boston Marriage (1999), a historical squib about early 20th-century lesbians; and then Romance (2006), a broad legal farce. Including November, Race and The Anarchist, Mamet has now had six critical and/or box-office disappointments in a row.

So what has happened to Mamet? In one sense, he is indeed carrying on a great tradition: late-period collapse. Only one of the 18 plays Miller wrote in his last 34 years, Broken Glass, has the slightest claim to rival Death of a Salesman, The Crucible and All My Sons. Even more grimly, all 17 plays of Tennessee Williams's last two decades seem doomed to spend their lives in university archives rather than regularly on stage. The graph of a playwright's life – especially in the commercially driven US – seems to be that, as the author gets older, scripts lose energy and audiences lose interest.

And yet Mamet is an unusual case. Whereas Miller and Williams's new work was ostracised by Broadway, Mamet's long succession of problem pieces have had high-budget, starry New York premieres. And that, I think, has been the problem. Whereas earlier great American playwrights were victims of becoming unbankable, Mamet has suffered, perversely, from the opposite problem. Because producers continue to want to fund his work and major actors to perform it, he has begun to write the sort of high-concept, talking-point plays that Broadway economics demand – although, as he has found, most attempts to create one will fail.

Britain's culture secretary, Maria Miller, keeps asking theatre to come up with arguments to justify subsidy; perhaps someone should send her a bound copy of Mamet's last six plays. Would we have had Stoppard's Arcadia, Bennett's The History Boys and Churchill's Love and Information if these playwrights had been required to launch them, cold, in the West End? Consciously or subconsciously, Mamet seems to me to have been coarsened by financial pressure.

His early plays were driven by language and character. An astonishing ability to turn everyday exchanges and expletives into poetry was captured in a 1980s New York joke, in which a down-and-out asks a Manhattan passer-by for cash. Refusing, the rich man says: "Neither a borrower nor a lender be – Shakespeare", to which the beggar replies: "Go fuck yourself – David Mamet."American Buffalo and Glengarry Glen Ross are regularly revived because they contain the best imaginative representation of real-life conversation since Harold Pinter; characters such as the thief Teach and the real-estate salesman Shelley Levene are distinctive but representative Americans in the tradition of Miller's Willy Loman.

In his later work, though, Mamet seems to begin not with a location or protagonist but with a theme. The subject matter of Race is baldly stated in the title; November might just as well have been called Politics. And, while the early work contains arguments between characters, the recent plays seem more engaged in disagreement with the audience. This war was openly declared in his 2008 hand-grenade of an essay, "Why I Am No Longer a Brain-Dead Liberal". Tom Wolfe has described himself as the only Republican in American literature; Mamet shows increasing signs of doubling the number.

Rarely granting interviews, the playwright now seems to view himself as a lone and besieged voice in US theatre. The published acting edition of Race even contains a "Talkback Restriction" warning that: "Until two (2) hours after the end of each performance of the Play, no presentation, performance or discussion of any type related to the Play, other than the Play as written by the Author, shall be conducted or authorized by the licensee in any venue." Anyone who breaches this rule will be required to "pay to David Mamet the sum of $25,000".

It seems strange that the most talked-about writer in modern American theatre should be so concerned to stop people talking about his plays. As one of his characters might put it: What the fuck happened?

• This article was amended on 13 June 2013. The original misspelled Debra Winger's forename as Deborah.