Can we count the Firesign Theatre as a “band”?
(Smacks head)
Aerosmith was formed in 1970 so it’s not a sixties band. But all of its members, past and present, are still alive.
Another near-sixties band - all of the Eagles (formed in 1971) are still alive.
The Holy Modal Rounders. I think. (Peter Stampfel has a shot at being the most well-known person without a Wikipedia page.)
At least one of the guys on Safe As Milk is dead, but the lineup of Captain Beefheart’s Magic Band circa Trout Mask Replica are all alive.
(OK, those 2 are pretty obscure.)
Surprised that two founding members of Buffalo Springfield are deceased. And I was going to go with The New Lost City Ramblers, formed 1958, but apparently Mike Seeger died a few months ago. Sorry to hear it.
Scorpions
I think all of the members of Gerry & the Pacemakers (formed in 1959) are still alive. Gerry Marsden, Freddie Marsden, Les Chadwick, and Les Maguire all are. But while I couldn’t find any mention of Arthur Mack’s death I also couldn’t confirm he’s still living.
Sorry. While doing some more searching for Mack, I found out that my information on Freddie Marsden is out of date. He died in 2006.
Kraftwerk formed in 1970, although the two founders Florian Schneider and Ralf Hutter had collaborated in other groups before this. They are both still alive although Florian is no longer in the group.
Alvin Lee, Ric Lee, Chick Churchill, and Leo Lyons - the original members of Ten Years After - are all still with us.
Simon, Alvin, and Theodore are all still alive and the Chipmunks were founded in 1958.
But David Seville* died long ago.
All members of Pentangle (first album: 1968) are still alive.
For a group better known for hits, there’s the The Spencer Davis Group (“I’m a Man” and “Gimme Some Loving”)
*Cousin to William Saroyan, Seville (nee Ross Bagdasarian) also appeared in Hitchcock’s rear window as the composer character.
Creedence Clearwater Revival John Fogerty, Stu Cook and Doug Clifford are still alive
Tom Fogerty died in 1990
CCR played at Woodstock but they aren’t in the documentary movie.
Steely Dan.
Mr. Fagen and Mr. Becker are very much alive - they rocked my socks off last Saturday night 
Their original bassist (who left the group within two years of their formation) is dead, but otherwise, The Moody Blues members are all still alive and kicking.
Jefferson Airplane
Nope. Both original drummer Skip Spence and his replacement, Spencer Dryden, are dead.
The Doors!
Elvis!
(They tour regularly. Andy Kaufman warms up the crowd.)
Given that the OP specifies bands that formed in the 1960’s, and that most founding band members are in their 20’s, most of these people are approaching or in their 70’s.
Even ignoring the stresses of the ‘rock star’ lifestyle, just looking at the life expectancy of males born in the 1940’s, you would expect to see many of them dying about now.