On the bar of a pub in Manchester city centre where I drink regularly is a tap for Bass XXXX, a keg mild. Another pub in East Manchester I go to occasionally has another, Mann's Chestnut Mild. I have never seen anyone order a pint of either.
Neither Bass nor Mann's have been independent breweries for a long time. Mann's merged with Watneys in 1958 and Bass was taken over by Interbrew in 2000. Their brands are now part of the portfolio of global brewers Diageo (best known for Guinness) and A-B Inbev (whose flagship "beer" is Budweiser). I'd guess that neither of them have any interest in mild and have them contract brewed, presumably in very small quantities.
Kegs unlike casks don't have a spile hole through with carbon dioxide is vented and oxygen enters. They remain pressurised after they've been tapped and therefore slow turnover isn't a problem like it is with cask beer. I wonder how long keg beer keeps after being tapped. In theory, you'd think for ever. But I'd be interested to hear from a publican, scientist or other expert if it actually does.