I'm surprised no one has mentioned these two yet:
Cheers: Nicholas Colasanto ("Coach") (d. Feb. 1985)
Sesame Street: Will Lee (Mr. Hooper aka "Mr. Looper" by Big Bird) (d. Dec. 1982)
Also on "Sesame Street," Northern Callaway, who played David (who succeeded Mr. Hooper as the owner to Hooper's Store) passed away himself in 1990, but IIRC the script mentioned that he "moved to his grandmother's farm" (and his death was not mentioned).
Also for "Sesame Street," one could go as far to include Jim Henson in this list (he died May 16, 1990--the same day as Sammy Davis Jr.). At the same time, "Muppet Babies" was still airing on CBS Saturday mornings.
Another cartoon voice who passed away while his show was on the air:Wuzzles
(CBS 1985-86, ABC reruns '86-87): Bill Scott, the voice of Moosel. I have seem some claims that more episodes of the "Wuzzles" than the original 13 were to be produced for a second season in 1986 (and there were additional Wuzzle characters that came out in dolls and books than the original 6 that IMO probably would have been introduced to the show had there been a second season), but never occurred after Scott's death.