Leonard Nimoy as Spock: 18 years between The Undiscovered Country and Star Trek 2009
Harrison Ford as Indiana Jones: 19 years between The Last Crusade and KOTCS
Harrison Ford as Han Solo, Mark Hamill as Luke Skywalker, and Carrie Fisher as Leia Organa: 32 years between ROTJ and TFA
Dolph Lundgren as Ivan Drago: 33 years between Rocky IV and Creed II
Billy Dee Williams as Lando Calrissian: 36 years between ROTJ and TROS
What do you think? Can Burt's stretch of time be topped?
As Burt played Robin/Dick Grayson in Legend of the Superheroes (as you said) then that's 2 years less.
I suppose if we were to frame it differently - timespan from first appearance to most recent, the numbers would again skew in Burt's favor. 1966 - 2019 = 53 years. That one's pretty hard to top, though Nimoy would come close. If you count the start of production on The Cage in 1964, he played Spock over a span of 49 years, until Star Trek Into Darkness.
Next after Nimoy would probably be the six cast members of The Dick Van Dyke Show who reprised their roles in the 2004 TV-movie The Dick Van Dyke Show Revisited - 43 years.
One of my favorites has always been Paul Newman in "The Hustler" (1961) and "The Color of Money (1986) at 25 years.
Tom Cruise will have a long stretch when Top Gun II is finally released too.
And in terms of a timespan of appearances... My favorite is Desmond Llewelyn as "Q" starting in 1963 in "From Russia with Love" and ending in 1999 with "The World is Not Enough". He played the part every few years without any major gaps.
I also found myself scratching my head over the appearance of Robert Wuhl as Alexander Knox. He's reading a newspaper stating that Batman has captured the Joker. When did that happen? And wouldn't this be Earth-89 30 years later, with the Joker long dead? A rumor had suggested that the newspaper headline would be about Bruce & Selina getting married. That would have been more satisfying.
Oh well. Here's hoping Brandon Routh as Superman has something useful to do!