Cliff Richard And The Shadows have done pretty well, they formed in 1958 and only the original bassist is no longer alive. The surviving original Shadows apparently performed for a documentary last year.
Wonder how many bands have now lost everyone? That question came up when the last of the Jimi Hendrix experience died (Mitch Mitchell in 2008). If they weren't the first they were one of them.
I remember on the Prindle site had the Rolling Stones as as the oldest rock band other than the Ventures, but it looks like they've outlasted them as well - the main member of the band is a guy who's only been involved since 1980.