This is not /r/Politics people. Please make sure you answer with a lot more than just your opinion.

He was a Kennedy in Massachusetts in the late 1960s.

http://en.wikipedia.org/wiki/Electoral_history_of_Ted_Kennedy

He was up for re-election in 1970. You can see that year his vote share took a dive, how much of that is to be blamed on Chapaquiddick I couldn't say, but basically if he can win in 1970 he has 6 years to move past the incident. Which evidently he did if you look at the vote share he got in 1976.

Basically it comes down to it being very difficult to beat a Senate incumbent in a state that leans heavily towards their party. Kennedy in Massachusetts is probably one of the more extreme examples you could think of having that kind of home field advantage.