Our national collections have snubbed them, and the genre's heavyweight American champions are either dead or have stopped buying. The late Jack Dick, a Connecticut cattle-breeder with a 10-gallon hat and a fortune made by pioneering artificial insemination, bought heavily in the Sixties; but he became financially unstuck, and the whole lot was dumped into a series of Sotheby's sales in London.
Paul Mellon, the American billionaire, first bought as an Oxford undergraduate in the Twenties, and continued into the Eighties. His sale at Christie's in 1989 was London's last auction dedicated exclusively to sporting pictures.
In the Eighties, Christie's and Sotheby's held massive annual sporting sales in New York. Now only Sotheby's keeps the flag flying in the US market, with a modest sale in New York in June.
When Ackermann, the two-centuries-old sporting picture dealers to the nobility, folded two years ago, followed by Leggatt Brothers, it looked as if the stable door was closed.
Huntin', racin', shootin' and fishin' paintings are now lumped together by London auctioneers under the heading 'British pictures', and prices have dropped by up to one-third since the market peak of 1988-89.
Expensive sporting paintings capable of perking up the market are mostly locked away in American museums or private collections. Demand is down, prices are down and the anti-blood-sport lobby is not helping the market.
So is this the time to throw money into the mire? At least sporting paintings are no longer prone to boom and bust, and their price drop has been less severe than that in other sectors of the picture market.
It is a genuine collectors' market. American enthusiasts, especially on the East Coast, pride themselves on being more British than the British, and are sufficiently well-heeled to maintain a steady flow of money for purchases.
Now that dollars can buy more pounds, auctioneers are reporting more dollar transactions for sporting paintings. The past two months' sudden upturn for Victorian paintings in general has been dollar-led.
Peter Johnson, of Ackermann and Johnson, which took over Ackermann's stock, has reported unprecedented Continental interest: a hefty Belgian deal in sporting paintings and sales in France, Italy, the Netherlands and Spain.
'It has never happened before,' he says. 'Suddenly, Continental buyers have realised that this art is unique to this country.'
The top six artists in the field are Herring (junior and senior), Ferneley, Marshall, Stubbs and Agasse. On past form, a tip-top Stubbs could fetch pounds 500,000, and a top Herring Snr about pounds 400,000 (the record is pounds 600,000). In recent years, competent Herrings have gone for under pounds 30,000.
Richard Green, a London dealer, reckons that it would still cost at least pounds 100,000 to buy a fine Herring Snr of a Derby winner. A small but acceptable Herring might cost pounds 20,000, and he considered that there could be nothing decent under pounds 5,000-pounds 10,000.
Look for paintings with identifiable characters, or which are 'of interest', he advises; such as the topographical interest of a Pollard showing the Royal Mail post chaise in the snow at York post office.
For the rest of us, there are six British and Old Master sales a year at Christie's South Kensington, with prices under pounds 1,500. Bonhams Chelsea has four down-market 'sporting sales' a year (including sporting memorabilia) with prices in the hundreds. Alistair Scott, of Bonhams, says the anti-blood-sport stigma attaches only to the most gruesome: bear-baiting and cock-fighting.
Last November's British picture sale at Christie's registered the first fillip since the market failed. The firm's auctioneers are hoping that its 7 April sale (11am), the first of three annual sales, will herald the start of a gradual upturn.
Estimates for top lots are certainly bullish, such as the pounds 300,000-pounds 500,000 for a full-length portrait by Sir Thomas Lawrence of John Allnutt with his horse (1773-1863). A John Ferneley Snr of the Hon Henry Augustus Craven clearing a brook, with Belvoir Castle beyond, is estimated at pounds 100,000-pounds 200,000.
Sotheby's sale the previous day, also the first of an annual three, contains works of lesser quality and few sporting pictures. But for pounds 1,200-pounds 1,800 there is an oil, typical of the genre, attributed to the early 19th-century artist Samuel Spode, showing hunters jumping a ditch; and, for an estimated pounds 6,000-pounds 8,000, a young boy on a pony by Francis Calcraft Turner (1795-1846).
At the lower but respectable end of the market, Dendy Easton of Sotheby's Billingshurst, Sussex, pooh-poohs Mr Green's 'nothing decent under pounds 5,000-pounds 10,000'. For pounds 300-pounds 500, he says, you can pick up a presentable John Beer racing scene, or a Phillip Rideout, two popular down-market names. Billingshurst's next big annual sale, with 200-300 lots, is on 27 July at 10.30am.
British Sporting Art Trust, The Granary, South Street, Mayfield, Sussex TN20 6DB ( pounds 5 joining fee, annual subcription pounds 15, OAPs pounds 10).
Auction database statistics: Thesaurus (071-487 3401).