The tournament was first held in 1978 and in its early years could claim to be one of the biggest on the women's Tour outside the Grand Slams. In the 1980 final Martina Navratilova beat Chris Evert to replace her as world No 1. The next year Sue Barker's victory widened its appeal to a British audience.
For most of the last decade Steffi Graf has been the tournament's mainstay, reminding people every year that one of the reasons she liked coming was that she was left in peace when she looked round the town's antiques shops. That, it now seems, may have been more a case of indifference than politeness.
Past sponsors have included Daihatsu, Pretty Polly and Midland Bank. In 1993 Autoglass took over but, Hendon says, decided "it wasn't quite the way they wanted to go". Last year, for the first time, there was no sponsor, and nor will there be this year in spite of the efforts of Hendon and the Lawn Tennis Association, which is underwriting the event.
"We feel this may be a consequence of not having any British players to take part," Hendon says. "When there is so much patriotism in sport, it's sad that we don't have the players to excite the public."
John Feaver, director of events at the LTA, says Brighton has "lost its polish", and with prize money increasing - up from $50,000 to $430,000 [pounds 280,000] in 17 years - the LTA no longer wants to meet costs that would otherwise be borne by a sponsor. So it has sold Brighton and bought a men's clay court event that until now has taken place in Bordeaux. From next year it will be played in Bournemouth in early September.
With five Britons in the world's top 150 and the arrival of Greg Rusedski, Feaver feels the men's domestic scene has more "credibility" than the women's. Now he must convince a potential sponsor - or more likely, sponsors - of that.