If it makes ya feel any better I have the same problem with my 327 62 SS. Thinking it was probably the starter getting weak as it looks to be the original. Haven't tried any of the remedies mentioned here as yet.
Bruce Old Toy: Ol' Betsy stock 59 Apache SB Stepside (Gone but not Forgotten) New Toy: 1962 Impala SS Coupe The Driver: 1990 Toyota truck