I recall 'Newhart' had a short run in syndication in about 1986 or '87. While the series as a whole has been regarded very highly by pop culture writers in the last 20 years or so, when 'Newhart' first went into off-network reruns, it may have suffered a bit in comparison with the '70s 'Bob Newhart Show'. On the other haand, 'Newhart' was still doing well on CBS at that point. Maybe the reruns were a little too 'fresh'?
Another '80s hit that basically went nowhere in syndication was 'The Cosby Show'. Long before Cosby's personal life sank him, and this series, without a trace, 'The Cosby Show' made news for a lucrative contract for the rights to reruns of the first few seasons, But within a few months, viewers were tired of the older episodes...and not long after, the still-sizable NBC audience began to decline, as well.
When the "Cosby Show" went into off-network syndication in 1988, stations like WWOR and KCOP (both before they came under the same ownership) paid hundreds of thousands of dollars PER EPISODE to carry the show; I remember seeing WWOR paying about $460,000 per episode (and up to that point when it entered syndication, only four seasons have been produced). I wouldn't call the "Cosby Show" reruns in off-net syndication a failure...hell, there were stations still the show up until his legal troubles arised.