Oh! I've seen this before! There's a bit in the FAQ about Rockefeller, Romney, and someone else going ham on Nixon! Let me try to dig it up.

Edit: I found it!! u/Samuel_Gompers wrote this series of posts:

https://www.reddit.com/r/AskHistorians/comments/1nolzz/comment/cckrkh5

turns out they were going ham on Barry Goldwater but the post goes into more detail on the Nixon ordeal

edit again: I totally forgot that the post discusses probably the most notable instance of someone in the Republican party preventing the incumbent from being re-elected - Teddy Roosevelt tried his hardest to prevent Taft from getting nominated then left the Republican party to run against Taft, leading to Wilson becoming president