Back in the old days (at least according to my parents), as soon as a show became unprofitable, it was yanked off the air. That's why on old episodes of Password Plus and other network game shows, they were constantly urging you to tune in, tell your friends, etc. I remember on $25,000 Pyramid (I can't remember if it was the beginning of the 80's run or the time it returned from hiatus due to Wipeout's wipeout) where Dick Clark pleaded with the viewers to contact their friends and say that the show was back on the air.
Nowadays, since nearly everything is syndicated, I think it usually goes by mid-season and full-season replacement. However, the last version of Card Sharks didn't even make it to mid-season, IIRC. Perhaps someone more confident than me should be speaking about this.