Like Chico and the Man, a lot of the humour on "Gimme a Break" revolved around the friction of it's leads, in this case Nell Carter and Dolph Sweet. So when Sweet passed away from stomach cancer after the fourth season, the show completely lost it's bearings.
This lead to the show to slowly get rid of much of the supporting characters, namely the chief's daughters and co-workers and just like Chico and the Man, start adding some cutsey poo kids (The Lawrence brothers who would continue to plague tv for over a decade afterwards) to brighten things up.
In the end, the show had Nell, Addy, grandpa and the boys living in New York City with Nell's mother and a cast of wacky neighbours. It didn't resemble the series it once was at all, it's like biting into a mars bar and finding honey mustard. There was no longer a need to give breaks, so why go on?