I don't know about whether this people choose to exercise their rematch clause because there may not have been one but, here is a list of controversial decisions where there was no rematch:
Whitaker vs Chavez Sr
Williams vs Lara (world title eliminator)
Foreman vs Briggs
Pernell whitaker vs. JCC sr. He never avenged the robbery.
Many have been robbed and failed to get the rematch. Pernell Whitaker never avenged any of his robberies. Not sure whether he tried to obtain a rematch or not with ODLH or JCCSnr.
Marvelous Hagler Sugar Ray leonard
I heard that Titties Trinidad was somehow cheated by the American Bernard Hopkins.
Please inform me of some of the most popular boxers throughout recent history (70's til present) that got robbed by the judges of a clear victory, & chose not to exercise their rematch clause?