Brezhnev had a heart attack in 1974* and a stroke in 1976 and from then point onwards got increasingly ineffective afterwards. This played out in his rule, with Andropov and the KGB being strongly relieved when he finally died and they could focus on ruling the nation.
http://articles.latimes.com/1988-09-07/news/mn-1657_1_brezhnev-historian-rule
I'm not sure if a more healthy Brezhnev would stop the stagnation wholesale, but could he at least rule more effectively.
*I and a couple of Soviet historians suspect-though I can't prove-that his health was not helped by the resignations of Willy Brandt and Richard Nixon, which Brezhnev (a rather impulsive, emotional fellow) took
very hard as he considered both men close colleagues, and even friends (or as close to that as a Soviet leader could have abroad, I guess). Especially since his political well being was staked on detente, and Soviet politics, while less lethal, was still unkind to losers.
Brezhnev detested Honecker, interestingly enough, and preferred to deal with the West Germans. This had a strong impact on East German foreign policy, and indeed the course of detente itself. Remember, Brandt was taken down because of the Stasi spy scandal-Brezhnev would have been pretty disturbed by that. As for the latter, I've already explained that Brezhnev (and many older Russians
to this day) took Watergate as proof of shadowy circles in the US determined to wreck Presidents who didn't toe the line. They just refuse to believe that a high horsepower statesman really had to resign over something as "mundane" as spying on his opponents.